Banach Lattices 1 Riesz Spaces 1.1 Basic Properties of Riesz Spaces and Banach Lattices 1.2 Sublattices Ideals and Bands 1.3 Regular Operators and Order Bounded Functionals 1.4 Duality of Riesz Spaces the Nakano Theory 1.5 Extensions of Positive Operators 2 Classical Banach Lattices 2.1 C(K) Spaces and M Spaces 2.2 Complex Riesz Spaces 2.3 Disjoint Sequences and Approximately Order Bounded Sets 2.4 Order Continuity of the Norm KB Spaces and the Fatou Property 2.5 Weak Compactness 2.6 Banach Function Spaces 2.7 Lp Spaces and Related Results 2.8 Cone p Absolutely Summing Operators and p Subadditive Norms 3 Operators on Riesz Spaces and Banach Lattices 3.1 Disjointness Preserving Operators and Orthomorphisms on Riesz Spaces 3.2 Operators on L and M Spaces 3.3 Kernel Operators 3.4 Order Weakly Compact Operators 3.5 Weakly Compact Operators 3.6 Approximately Order Bounded Operators 3.7 Compact Operators and Dunford Pettis Operators 3.8 Tensor Products of Banach Lattices 3.9 Vector Measures and Vectorial Integration 4 Spectral Theory of Positive Operators 4.1 Spectral Properties of Positive Linear Operators 4.2 Irreducible Operators 4.3 Measures of Non Compactness 4.4 Local Spectral Theory for Positive Operators 4.5 Order Spectrum of Regular Operators 4.6 Disjointness Preserving Operators and the Zero Two Law 5 Structures in Banach Lattices 5.1 Banach Space Properties of Banach Lattices 5.2 Banach Lattices with Subspaces Isomorphic to C() C(0 l) and L1(0 1) 5.3 Grothendieck Spaces 5.4 Radon Nikodym Property in Banach Lattices References.