Lectures on Nonextensive Statistical Mechanics -- I. Nonextensive Statistical Mechanics and Thermodynamics: Historical Background and Present Status -- II. Quantum Density Matrix Description of Nonextensive Systems -- III. Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations -- IV. ComputationalMetho ds for the Simulation of Classical and Quantum Many Body Systems Arising from Nonextensive Thermostatistics -- Further Topics -- V. Correlation Induced by Nonextensivity and the Zeroth Law of Thermodynamics -- VI. Dynamic and Thermodynamic Stability of Nonextensive Systems -- VII. Generalized Simulated Annealing Algorithms Using Tsallis Statistics: Application to ±J Spin Glass Model -- VIII. Protein Folding Simulations by a Generalized-Ensemble Algorithm Based on Tsallis Statistics.