The book surveys mathematical relations between classical and quantum mechanics, gravity, time and thermodynamics from various points of view and many sources (with appropriate attribution). The emergence theme is developed with an emphasis on the meaning via mathematics. A background theme of Bohemian mechanics and connections to the quantum equivalence principle of Matone et al. is also developed in great detail. Some original work relating the quantum potential and Ricci flow is also included.Contents:Some Quantum BackgroundSome Geometric AspectsAspects of EmergenceKaluza–Klein and CosmologyRemarks on Thermodynamics and GravityGeometry and MechanicsOn Time and the UniverseGravity and the Quantum PotentialReadership: Researchers and graduate students in mathematics, applied mathematics, probability and statistics, theoretical physics and chemistry, quantum physics, astrophysics and cosmology, and philosophy.