1 Non-triviality of Arithmetic Invariants.- 2 Elliptic Curves and Modular Forms.- 3 Invariants, Shimura Variety and Hecke Algebra.- 4 Review of Scheme Theory.- 5 Geometry of Variety.- 6 Elliptic and Modular Curves over Rings.- 7 Modular Curves as Shimura Variety.- 8 Non-vanishing Modulo p of Hecke L-values.- 9 p-Adic Hecke L-functions and their μ-invariants.- 10 Toric Subschemes in a Split Formal Torus.-...