  These lecture notes are intended as a guide to Graduate level readers that
are already familiar with basic General Relativity. They present in a concise
way some advanced concepts and problems encountered in the study of
gravitation. In these notes are covered: Alternates forms of the Schwarzschild
Black Hole solution, including the classic Kruskal extension; An account of the
building of Conformal, Carter-Penrose, diagrams; A discussion of Birkhoff
Theorem; A discussion of tools for Geodesics and congruences, including Energy
Conditions; A discussion of Horizons and an approach to some of the singularity
theorems; An exploration of the Kerr Black Hole solution properties, including
the Penrose Process and Black Hole Thermodynamics; A discussion of the Eckart
and Israel-Stewart Relativistic Thermodynamics; A discussion of Tetrads in
Relativity, in Einstein-Cartan theory and in Newman-Penrose formalism; An
explicitation of calculations on Geodesics approach from Hamilton-Jacobi
Formalism; A derivation from Least action of the equation of Motion of a top in
Relativity, the M.P.D. equations
