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We present the goals, strategy and first results of the high-cadence Galactic plane survey using the Zwicky Transient Facility (ZTF). The goal of the survey is to unveil the Galactic population of short-period variable stars, including short period binaries and stellar pulsators with periods less than a few hours. Between June 2018 and January 2019, we observed 64 ZTF fields resulting in 2990 deg2 of high stellar density in ZTF-r band along the Galactic Plane. Each field was observed continuously for 1.5 to 6 hrs with a cadence of 40 sec. Most fields have between 200 and 400 observations obtained over 2-3 continuous nights. As part of this survey we extract a total of ≈230 million individual objects with at least 80 epochs obtained during the high-cadence Galactic Plane survey reaching an average depth of ZTF-r ≈20.5 mag. For four selected fields with 2 million to 10 million individual objects per field we calculate different variability statistics and find that ≈1-2% of the objects are astrophysically variable over the observed period. We present a progress report on recent discoveries, including a new class of compact pulsators, the first members of a new class of Roche Lobe filling hot subdwarf binaries as well as new ultracompact double white dwarfs and flaring stars. Finally we present a sample of 12 new single-mode hot subdwarf B-star pulsators with pulsation amplitudes between ZTF-r = 20-76 mmag and pulsation periods between P = 5.8-16 min with a strong cluster of systems with periods ≈ 6 min. All of the data have now been released in either ZTF Data Release 3 or data release 4.