The number of known periodic variables has grown rapidly in recent years. Thanks to its large field of view and faint limiting magnitude, the Zwicky Transient Facility (ZTF) offers a unique opportunity to detect variable stars in the northern sky. Here, we exploit ZTF Data Release 2 (DR2) to search for and classify variables down to r ~ 20.6 mag. We classify 781,602 periodic variables into 11 main types using an improved classification method. Comparison with previously published catalogs shows that 621,702 objects (79.5%) are newly discovered or newly classified, including ~700 Cepheids, ~5000 RR Lyrae stars, ~15,000 Delta Scuti variables, ~350,000 eclipsing binaries, ~100,000 long-period variables, and about 150,000 rotational variables. The typical misclassification rate and period accuracy are on the order of 2% and 99%, respectively. 74% of our variables are located at Galactic latitudes, $|b|<10^circ$. This large sample of Cepheids, RR Lyrae, Delta Scuti stars, and contact (EW-type) eclipsing binaries is helpful to investigate the Galaxys disk structure and evolution with an improved completeness, areal coverage, and age resolution. Specifically, the northern warp and the disks edge at distances of 15--20 kpc are significantly better covered than previously. Among rotational variables, RS Canum Venaticorum and BY Draconis-type variables can be separated easily. Our knowledge of stellar chromospheric activity would benefit greatly from a statistical analysis of these types of variables.
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