Bitcoin Core is the widely used open-source Bitcoin software client that is the direct descendant of Satoshi Nakamoto's original software. Its code is hosted on GitHub, and readily compiled binaries can be found on the official Bitcoin Core site.
Bitcoin Core is a full node implementation—it downloads and validates all Bitcoin transactions and blocks, and allows the user to participate in consensus. We recommended starting with Bitcoin Core as it is the most popular software client and has many accessible help tutorials, despite other compatible implementations being available. It also gives you the highest degree of compatibility with the Bitcoin network.