Introduction to Algebraic Independence Theory

?(?, z) and Transcendence.- Mahler's conjecture and other transcendence Results.- Algebraic independence for values of Ramanujan Functions.- Some remarks on proofs of algebraic independence.- Elimination multihomogene.- Diophantine geometry.- Géométrie diophantienne multiprojective.- Criteria for algebraic independence.- Upper bounds for (geometric) Hilbert functions.- Multiplicity estimates for solutions of algebraic differential equations.- Zero Estimates on Commutative Algebraic Groups.- Measures of algebraic independence for Mahler functions.- Algebraic Independence in Algebraic Groups. Part 1: Small Transcendence Degrees.- Algebraic Independence in Algebraic Groups. Part II: Large Transcendence Degrees.- Some metric results in Transcendental Numbers Theory.- The Hilbert Nullstellensatz, Inequalities for Polynomials, and Algebraic Independence.