Arecibo is the biggest single-dish telescope in the World, thereby providing full spatial frequency coverage, high surface brightness sensitivity, and arcminute scale resolution at decimeter wavelengths - a unique and powerful combination. The ALFA system will allow these unique properties to be used to image large areas of the sky, thereby enabling new and exciting scientific directions. A continuum survey of the wider Galactic plane using the full ALFA band (1225 - 1525 MHz) would provide a unique database in a number of ways. Firstly, it would yield full spatial frequency mapping with unsurpassed resolution of extended features such as the Galactic background emission itself, HII complexes, and middle-aged and old SNRs, with simultaneously recorded linear polarization measurements being of especial importance. Many new extended, low-brightness objects can be expected to be found. Analysis of the variation of intensity as a function of frequency within the 300 MHz band and comparison with the existing Effelsberg Galactic plane surveys at 2.7 and 5.0 GHz would immediately allow accurate estimation of the spectral index distribution of individual objects, as well as of the radiation from the Galactic disc, providing the ability to perform an accurate and full thermal-nonthermal separation on angular scales of a few arcminutes. This would allow the study of energy injection and energy losses of relativistic particles in the ISM associated with SNR, and the mechanisms of vertical transport and diffusion of energy from the disk of the Galaxy to the halo and intergalactic space. The appearance of the polarized sky at 21 cm wavelength is surprising, and at first seems bewildering. As seen by both the Westerbork 327 MHz synthesis observations at high Galactic latitude and the Canadian Galactic Plane Survey with the DRAO Synthesis Telescope, there is no relationship between total intensity and polarization structures. We expect to detect supernova remnants as polarized objects, and the diffuse Galactic synchrotron emission, but the bulk of the area of the Galactic Plane when imaged at arcminute scales is filled with highly structured polarization emission with no counterpart in Stokes I. The accepted interpretation is that the distributed polarized emission arises from the Galactic synchrotron emission, which is intrinsically quite smooth. Differential Faraday rotation in the intervening magneto-ionic medium, the so-called Faraday Screen, imposes fine structure on the polarized emission. In fact the sky is dominated by the effects of this medium through which the signals have traveled rather than by intrinsic structure in the polarized synchrotron emission itself. This emerging field of study is gradually moving from phenomenology to astrophysics. The signatures of the Faraday polarization studies are revealing details of the magnetic field (rotation measures of compact sources) and of the magneto-ionic medium (imaging of extended emission). The signals produced by the Faraday Screen are very weak typically a few 100 mK at most (a fraction of the polarized signal from the synchrotron background). The limited surface brightness sensitivity of interferometric observations samples only the strongest features, and even in these areas, derived RM measures are very noisy due to low signal-to-noise per channel. Moreover the lack of zero-spacing flux in the interfermetric observations leads to complications in interpreting the polarization signals. The high brightness sensitivity of the Arecibo telescope coupled with the few arcminute beam size promises major advances in the study of the magneto-ionic medium, particularly at mid to high latitudes where the signals become weaker due to the fall off in the background synchrotron brightness. It is precisely in these latitude regions where critical information about the vertical structure of the Galactic magnetic field can be measured. At higher latitudes the magnetic field is even more significant in the energy budget of the ISM and is likely to play a dominant role in the vertical energy transport, and in the pressure equilibrium of the medium. Such studies are important in a wider context of the astrophysics of galaxies. The radio-infrared correlation of starburst and normal galaxies must be a result of the relationship between massive star formation and supernova rates in evolving galaxies. The radio luminosity resulting from injection of relativistic particles must in turn be related to both the life time of energetic particles and the rate of bulk flow of energy out of the galaxy. Both are directly linked to the galactic magnetic fields, in particular the vertical structure of the field. Apart from the polarized emission structure from the Galactic magnetio-ionic medium, Faraday Screen, the high latitude region visible from Arecibo contains known non-thermal emission structures. The North Polar Spur (Loop 1) runs along more than 6 hr of RA within the Arecibo sky. Lower resolution measurements have shown this object to contain rich small-scale structure, both on its main arc and in internal ridging. Above b = 45 deg, even the low resolution Dwingeloo measurements have shown this nearby (~100 pc distant), old SNR to be above 70% linearly polarized at 1.4 GHz. Full-Stokes mapping of the continuum emission of large, nearby, spiral galaxies and giant radio galaxies would add considerable information on the very extended structures and magnetic field configurations within these objects. The Arecibo continuum survey would also measure the polarized intensity of the many "point-like" background sources through the plane at both low and high latitudes. The sensitivity of Arecibo combined with the multiple channels across the 300-MHz bandwidth of ALFA would permit a complete RM survey to very low flux density levels and high RM accuracy. At low latitudes combination of RM estimates for SNRs and extragalactic sources seen through the plane with those measured for pulsars will allow modeling of the magnetic field distribution through the whole depth of the galactic disk (center and anticenter) visible from Arecibo. Studies of the change in RM as a function of latitude will provide a measure of the total RM along lines of site that are also probed by the Faraday screen effect, thereby allowing a measure of the relative Faraday depth of the screen features. The Canadian Galactic Plane Survey with a continuum RMS noise of 300 microJy/beam obtains a grid of background sources with sufficient polarized flux to provide a reliable RM with an area density of about 1 per square degree, over the restricted latitude range of 8 degrees. The Arecibo survey, at three times the sensitivity, will provide an area density almost an order of magnitude higher, over a large range of latitudes and with very high RM precision, thereby probing the vertical structure of the Galactic magnetic field with unprecedented sensitivity, precision and latitude range. Finally, with multiple-passes of the survey region the Arecibo continuum survey would yield the most sensitive survey for variable and transient sources ever undertaken. Using difference techniques, variable sources will be detectable well below the confusion limit. Ideally we will be able to search to the noise limit of about 100 microJy/beam per pass of the region and detect variables at the level of about 500 microJy. The sky has never before been searched for variations systematically and over a large area to this depth. We will also search the Stokes V channel for evidence of highly circularly polarized sources such as pulsars and flares stars. The GALFA Continuum Transit Survey (GALFACTS) An example of what can be achieved with continuum mapping at Arectibo is shown by a recent study of the weak supernova remnant, G42.8+0.6, by Snezana Stanimirovic and her collaborators. The map was fully sampled, with orthogonally scanned coverages being taken. These orthogonal coverages were subsequently "basket-weaved" to obtain optimum zero levels. For an ALFA continuum survey we assume that a spectrometer would be available with about 1000 channels covering the full 300-MHz ALFA bandwidth, a full-Stokes capability, and the ability to dump data "slowly" (say, a few dumps per sec). If we assume a Nyquist sampling time of 1.33 sec (see below) and the expected ALFA System Equivalent Flux Density (SEFD) of ~3 Jy, then combining both polarizations would give an rms noise of about 100 microJy/beam on cold sky. I Stokes-I this would be well above the confusion level due to the point source background RMS(confusion)~2 mJy/beam, implying the weakest believable detections at S(min)~10 mJy/beam (Fig. 4). However, the confusion level in polarization will be well below this value (about a factor of 100 less 20 microJy/beam). Hence, we can certainly make a very sensitive survey of polarization. For the diffuse Faraday Screen signals with no counterpart in Stokes I the spurious polarization will not generally be a problem. To measure polarization percentages will we must deal with the high spurious polarization responses expected for ALFA. It is not clear to what degree spurious polarization will affect RM measurements, since RM is derived form the frequency dependence of the polarized signal across the band. We will measure the effect of systematics on RM as part of the pilot project described in the next secion. To emphasize the power of having available a 300-MHz bandwidth for polarization measurements, the change of position angle across the band is Del=3.75*RM deg, (or one full 180 deg turn for an RM of 50 rad/m^2). The relatively small spectrometer channel width would prevent decorrelation across a channel, with Del(Theta)=0.004*RM deg for each 300-kHz channel. The biggest problems for any ALFA continuum survey would be; a) temporal zero-level drifts along a scan, b) the ~8-dB coma lobes for the outer horns, and c) the high spurious polarization responses. The most satisfactory way to deal with temporal zero-level drifts is to minimize them by scanning the telescope beam across the sky as fast as possible. However, dealwith the sidelobes and polarization artifacts, the data needs to be acquired as systematically as possible. An attractive possibility for achieving this is to fix the telescope on the prime meridian and NOD it in zenith angle at the maximum drive rate of 2.4 deg/min (to minimizing drifts). The scan pattern projected on the sky is then a zig-zag, where each "zig" is crossed by many "zags". This permits the minimization of residual zero level drifts through "basket-weaving". With such an observing strategy the variations of Tsys, antenna gain, sidelobe pattern, and spurious polarization are now purely dependent on declination (because on the meridian, zenith angle maps into declination), and their characterization and correction is much simplified. For example, if one can characterize the coma lobe patterns for all feeds such that they can be interpolated to 10% at any declination (i.e. zenith angle), then the 8-dB spurious responses could be reduced through CLEANing to some 18 dB. This is similar to, or better, than the normal Effelsberg beam. The meridian NODding technique has the additional benefit that all sky positions are observed with the telescope at the minimum possible zenith angle, thus minimizing the SEFD and maximizing the sensitivity. With the NODding approach suggested above, each zig and each zag would take about 2/3 sec to cross a Nyquist sampling interval. Hence, after averaging the (fully sampled) map of "zigs", and map of "zags", there would be an integration time of 1.33 sec per Nyquist interval. From this, the time to map the whole Arecibo sky would be about 1000 hr. The time to map smaller areas would be proportionally less, e.g. 100 hr to cover a 2.5 hr x 40 deg strip containing the inner Galactic plane. GALFACTS Pilot Observations The GALFA Continuum Survey group will propose for a pilot observation using the current single feed L-band system. We will observe a 1x10 degree area of the sky at mid-latitudes using the observing technique described above. The region will be observed twice (two independent passes), with each pass taking 20 hours. The observation region will be chosen to contain a strong compact source with known polarization properties to assess the polarimetric response of the system. However, we will also image the effects of the Faraday screen RM variations which occur in the absence of corresponding polarized signals and are thus largely independent of the Stokes I leakage terms. Comparison of the two images will provide an assessment of the reliability and reproducibility of the results, allow refinements of the processing and imaging techniques, and allow for algorithms for detection of variables and transient sources to be developed. We would use the available L-WIDE receiver and select 4 bands of 100 MHz each centered at 1170, 1410, 1510 and 1610 MHz, using an available combination of two front-end filters (1120-1220 MHz bandpass and 1320-MHz highpass filters) to eliminate the strong Radar-RFI. The IF filter would have 1 GHz bandwidth (1-2 GHz), instead of the usual 500 MHz BW, to allow the above bands without any in-band cutoffs. The WAPPS would be suitable backends, with 256 channels per 100-MHz band and about 2 millisecond integration (9-level sampling at input, and 32-bit output), for recording full Stokes parameters. Continuous switching correlated CAL (switching rate: 25 Hz; Step-size: 2 K) would enable monitoring of gain & system temperature variations for the two polarization channels. Commensality of the GALFA Continuum Survey with other Surveys The possibility of commensality with other ALFA surveys for a GALFA continuum survey needs to be considered. An immediate constraint is that no ALFA survey can easily be commensal with any other that requires the same spectrometer. A GALFA continuum survey would need the same 300-MHz bandwidth spectrometer as is planned for the pulsar search projects (only with full Stokes capability). As those pulsar search projects suggested to date all need relatively long integration times of at least a few minutes, while a continuum survey would collect data as rapidly as the telescope can be practically driven, the two classes of survey are not candidates for mutual commensality. While the proposed recombination-line ALFA survey uses a different spectrometer to the continuum survey, it again requires relatively long integration times, and does not seem suitable for mutual commensality. The constraint of long integration times would also seem to eliminate the possibility of commensality with a number of the suggested E-ALFA projects, such as the deep surveys, a ZOA survey and a Virgo cluster survey. More promising as prospective partners for commensal observing with an ALFA continuum survey are the proposed Galactic HI survey, and the shallow all-sky extragalactic survey for galaxies ("ALFALFA"). Both propose to use a different spectrometer to the continuum survey, and both would have rather short integration times. In addition, the Galactic HI survey would clearly also benefit from acquiring its data as systematically as possible given the ALFA sidelobes and polarization artifacts, as would the continuum survey. Similar considerations could also benefit ALFALFA. Discussion now needs to take place between the proposers of these three surveys to see if two- (or three-) fold commensality is practical. In the possibility that commensality is possible with one or both of the above surveys, but that they require longer integration times than we are proposing for the continuum survey, there would be distinct benefits in arranging that a common observing strategy be chosen such that a number of passes are made to obtain the integration times required by the other (slower) surveys. The continuum data for the additional passes would then be obtained at no extra cost (the other survey/s would be observing anyway, and the continuum survey would literally "piggy-back"). To the other surveys, there would be the advantage that the probability of the data at a particular position being totally wiped out by RFI would be minimized by spreading the data-taking over several epochs, while an overall "first-look" could be obtained relatively rapidly, with sensitivity then being improved in a uniform fashion by subsequent passes. For the continuum survey, a number of complete, uniformly taken, passes would have the great advantage that each (free) coverage would be individually mapped, and a systematic search of the Arecibo sky made for both total-intensity and polarization variable sources, plus transient emitters. Searching for transient radio continuum sources is a planned objective for the next generation of large telescopes such as LOFAR and the SKA.