The OGLE Collection of Variable Stars. Classical, Type II, and Anomalous Cepheids toward the Galactic Center

We present a collection of classical, type II, and anomalous Cepheids detected in the OGLE fields toward the Galactic center. The sample contains 87 classical Cepheids pulsating in one, two or three radial modes, 924 type II Cepheids divided into BL Her, W Vir, peculiar W Vir, and RV Tau stars, and 20 anomalous Cepheids - first such objects found in the Galactic bulge. Additionally, we upgrade the OGLE Collection of RR Lyr stars in the Galactic bulge by adding 828 newly identified variables. For all Cepheids and RR Lyr stars, we publish time-series VI photometry obtained during the OGLE-IV project, from 2010 through 2017. We discuss basic properties of our classical pulsators: their spatial distribution, light curve morphology, period-luminosity relations, and position in the Petersen diagram. We present the most interesting individual objects in our collection: a type II Cepheid with additional eclipsing modulation, W Vir stars with the period doubling effect and the RVb phenomenon, a mode-switching RR Lyr star, and a triple-mode anomalous RRd star.