1 Excessive Functions -- 1.1 Sub-Markovian resolvent of kernels -- 1.2 Basics on excessive functions -- 1.3 Fine topology -- 1.4 Excessive measures -- 1.5 Ray topology and compactification -- 1.6 The reduction operation and the associated capacities -- 1.7 Polar and semipolar sets. Nearly measurable functions -- 1.8 Probabilistic interpretations: Sub-Markovian resolvents and right processes -- 2 Cones of Potentials and H-Cones -- 2.1 Basics on cones of potentials and H-cones -- 2.2 ?-Balayages on cones of potentials -- 2.3 Balayages on H-cones -- 2.4 Quasi bounded, subtractive and regular elements of a cone of potentials -- 3 Fine Potential Theoretical Techniques -- 3.1 Cones of potentials associated with a sub-Markovian resolvent -- 3.2 Regular excessive functions, fine carrier and semipolarity -- 3.3 Representation of balayages on excessive measures -- 3.4 Quasi bounded, regular and subtractive excessive measures -- 3.5 Tightness for sub-Markovian resolvents -- 3.6 Localization in excessive functions and excessive measures -- 3.7 Probabilistic interpretations: Continuous additive functionals and standardness -- 4 Strongly Supermedian Functions and Kernels -- 4.1 Supermedian functionals -- 4.2 Supermedian ?-quasi kernels -- 4.3 Strongly supermedian functions -- 4.4 Fine densities -- 4.5 Probabilistic interpretations: Homogeneous random measures -- 5 Subordinate Resolvents -- 5.1 Weak subordination operators -- 5.2 Inverse subordination -- 5.3 Probabilistic interpretations: Multiplicative functionals -- 6 Revuz Correspondence -- 6.1 Revuz measures -- 6.2 Hypothesis (B) of Hunt -- 6.3 Smooth measures and sub-Markovian resolvents -- 6.4 Measure perturbation of sub-Markovian resolvents -- 6.5 Probabilistic interpretations: Positive left additive functionals -- 7 Resolvents under Weak Duality Hypothesis -- 7.1 Weak duality hypothesis -- 7.2 Natural potential kernels and the Revuz correspondence -- 7.3 Smooth and cosmooth measures -- 7.4 Subordinate resolvents in weak duality -- 7.5 Semi-Dirichlet forms -- 7.6 Weak duality induced by a semi-Dirichlet form -- 7.7 Probabilistic interpretations: Multiplicative functionals in weak duality -- A Appendix -- A.1 Complements on measure theory, kernels, Choquet boundary and capacity -- A.2 Complements on right processes -- A.4 Basics on coercive closed bilinear forms -- Notes