This chapter deals with the calculation of free energy differences (ΔF) by calorimetric thermodynamic integration (TI) – a general robust approach since the integration depends only on thermodynamic variables T, E etc., without the need to consider the microscopic structure of the system studied. This category includes Zwanzig’s free energy perturbation (FEP) and Kirkwood’s TI, where the integration variables are parameters of the Hamiltonian. To calculate the absolute F the integration should start from a reference state with known F. Two such integrations for a SAW and a peptide are carried out in detail. Thermodynamic cycles are described as a tool for comparing the free energy of binding of two of ligands bound to the same enzyme. Thus, ligand A is transformed by TI into ligand B in the solvent and the protein environments. The advantage of this process lies in its simplicity and the fact that only the ligand-environment interactions are involved. However, (1) the side chains (for example) are never equilibrated and the results keep changing as the simulation proceeds. (2) The integration variables (energies) might not provide enough guidance for the correct transformation of A into B in the protein. For example, the position of the transformed B in the active site and the number of water molecules there would be different than in the X-ray structure of the protein-B complex. The reverse transformations B → A can provide some estimation of the error involved.