The FourStar galaxy evolution survey (ZFOURGE) is a 45 night legacy program with the FourStar near-infrared camera on Magellan and one of the most sensitive surveys to date. ZFOURGE covers a total of $400 mathrm{arcmin}^2$ in cosmic fields CDFS, COSMOS and UDS, overlapping CANDELS. We present photometric catalogs comprising $>70,000$ galaxies, selected from ultradeep $K_s$-band detection images ($25.5-26.5$ AB mag, $5sigma$, total), and $>80%$ complete to $K_s<25.3-25.9$ AB. We use 5 near-IR medium-bandwidth filters ($J_1,J_2,J_3,H_s,H_l$) as well as broad-band $K_s$ at $1.05 - 2.16 mu m$ to $25-26$ AB at a seeing of $sim0.5$. Each field has ancillary imaging in $26-40$ filters at $0.3-8 mu m$. We derive photometric redshifts and stellar population properties. Comparing with spectroscopic redshifts indicates a photometric redshift uncertainty $sigma_z={0.010,0.009}$, and 0.011 in CDFS, COSMOS, and UDS. As spectroscopic samples are often biased towards bright and blue sources, we also inspect the photometric redshift differences between close pairs of galaxies, finding $sigma_{z,pairs}= 0.01-0.02$ at $1<z<2.5$. We quantify how $sigma_{z,pairs}$ depends on redshift, magnitude, SED type, and the inclusion of FourStar medium bands. $sigma_{z,pairs}$ is smallest for bright, blue star-forming samples, while red star-forming galaxies have the worst $sigma_{z,pairs}$. Including FourStar medium bands reduces $sigma_{z,pairs}$ by 50% at $1.5<z<2.5$. We calculate SFRs based on ultraviolet and ultradeep far-IR $Spitzer$/MIPS and Herschel/PACS data. We derive rest-frame $U-V$ and $V-J$ colors, and illustrate how these correlate with specific SFR and dust emission to $z=3.5$. We confirm the existence of quiescent galaxies at $zsim3$, demonstrating their SFRs are suppressed by $>times15$.
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