  We present a sample of Cepheid variable stars towards M31 based on the first
year of regular M31 observations of the PS1 survey in the r_P1 and i_P1
filters. We describe the selection procedure for Cepheid variable stars from
the overall variable source sample and develop an automatic classification
scheme using Fourier decomposition and the location of the instability strip.
We find 1440 fundamental mode (classical \delta) Cep stars, 126 Cepheids in the
first overtone mode, and 147 belonging to the Population II types. 296 Cepheids
could not be assigned to one of these classes and 354 Cepheids were found in
other surveys. These 2009 Cepheids constitute the largest Cepheid sample in M31
known so far and the full catalog is presented in this paper. We briefly
describe the properties of our sample in its spatial distribution throughout
the M31 galaxy, in its age properties, and we derive an apparent
period-luminosity relation (PLR) in our two bands. The Population I Cepheids
nicely follow the dust pattern of the M31 disk, whereas the 147 Type II
Cepheids are distributed throughout the halo of M31. We outline the time
evolution of the star formation in the major ring found previously and find an
age gradient. A comparison of our PLR to previous results indicates a curvature
term in the PLR.
