We present a catalog of 11 multi-planet systems from Campaigns 1 and 2 of the K2 mission. We report the sizes and orbits of 26 planets split between seven 2-planet systems and four 3-planet systems. These planets stem from a systematic search of the K2 photometry for all dwarf stars observed by K2 in these fields. We precisely characterized the host stars with adaptive optics imaging and analysis of high-resolution optical spectra from Keck/HIRES and medium-resolution spectra from IRTF/SpeX. We confirm two planet candidates by mass detection and validate the remaining 24 candidates to $>99%$ confidence. Thirteen planets were previously validated or confirmed by other studies and 24 were previously identified as planet candidates. The planets are mostly smaller than Neptune (21/26 planets) as in the Kepler mission and all have short periods ($P < 50$ d) due to the duration of the K2 photometry. The host stars are relatively bright (most have $Kp < 12.5$ mag) and are amenable to follow-up characterization. For K2-38, we measured precise radial velocities using Keck/HIRES and provide initial estimates of the planet masses. K2-38b is a short-period super-Earth with a radius of $1.55 pm 0.16~R_oplus$, a mass of $12.0 pm 2.9~M_oplus$, and a high density consistent with an iron-rich composition. The outer planet K2-38c is a lower density sub-Neptune-size planet with a radius of $2.42 pm 0.29~R_oplus$ and a mass of $9.9 pm 4.6~M_oplus$ that likely has a substantial envelope. This new planet sample demonstrates the capability of K2 to discover numerous planetary systems around bright stars.
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