Riemannian and semi-Riemannian geometry
Riemannian
do Carmo, Riemannian geometry
Petersen, Riemannian geometry
Geometric analysis
Jost, Riemannian geometry and geometric analysis
Aubin, Nonlinear analysis on manifolds. Monge-Ampere equations
Aubin, Some nonlinear problems in Riemannian geometry
Andews and Hopper, The Ricci flow in Riemannian geometry
Topping, Lectures on Ricci flow
Lin and Wang, The analysis of harmonic maps and their heat flows
Paul Minter's list of papers in geometric analysis
Semi-Riemannian and Lorentzian
O'Neill, Semi-Riemannian Geometry With Applications to Relativity
Javaloyes and Sanches, An Introduction to Lorentzian Geometry and its Applications
Beem, Ehrlich and Easley, Global Lorentzian Geometry