This clear and elegant text introduces Künneth, or bi-Lagrangian, geometry from the foundations up, beginning with a rapid introduction to symplectic geometry at a level suitable for undergraduate students. Unlike other books on this topic, it includes a systematic development of the foundations of Lagrangian foliations. The latter half of the text discusses Künneth geometry from the point of view of basic differential topology, featuring both new expositions of standard material and new material that has not previously appeared in book form. This subject, which has many interesting uses and applications in physics, is developed ab initio, without assuming any previous knowledge of pseudo-Riemannian or para-complex geometry. This book will serve both as a reference work for researchers, and as an invitation for graduate students to explore this field, with open problems included as inspiration for future research.

M.J.D. Hamilton has been teaching mathematics at all levels at Ludwig-Maximilians-Universität München and Universität Stuttgart for the past fifteen years. He is interested in the interactions of geometry and theoretical physics, and is known for his successful transfer of ideas between the two subjects. He is the author of the acclaimed textbook 'Mathematical Gauge Theory' (2017).

1. Introduction; 2. Linear algebra and bundle theory; 3. Symplectic geometry; 4. Foliations and connections; 5. Künneth structures; 6. The Künneth connection; 7. The curvature of a Künneth structure; 8. Hypersymplectic geometry; 9. Nilmanifolds; 10. Four-manifolds.