This book provides a foundation inspired by the mathematics of blockchain. It is inspired from a general analysis and synthesis of the current knowledge of blockchain technology and starts by laying a foundation for mathematics of Blockchain. The aim is for research in the area of blockchain to lead their study from the construction highlighted in this book.

First, the basis of a blockchain is set: block, transaction contents, block header, Merkle tree, nonce, Proof-of-Work. Connections with elliptic curves and cryptographic signatures is made.

Second, the book ties this with a Graph and Matrix Theories approach and models the peer-to-peer relationship through the Bitcoin Network.

Finally, the mathematical statements therein are proven and essential reminders can be found before each section, so the content can be accessible from a graduate level.