Tamari lattices originated from weakenings or reinterpretations of the familar associativity law. This was the subject of Dov Tamari's thesis at the Sorbonne in Paris in 1951 and the central theme of his subsequent mathematical work. Tamari lattices can be realized in terms of polytopes called associahedra, which in fact also appeared first in Tamari's thesis. By now these beautiful structures have made their appearance in many different areas of pure and applied mathematics, such as algebra, combinatorics, computer science, category theory, geometry, topology, and also in physics. Their interdisciplinary nature provides much fascination and value. On the occasion of Dov Tamari's centennial birthday, this book provides an introduction to topical research related to Tamari's work and ideas. Most of the articles collected in it are written in a way accessible to a wide audience of students and researchers in mathematics and mathematical physics and are accompanied by high quality illustrations.