1 Basic Concepts and Elementary Models. - 1. The Vocabulary of Probability Theory. - 2. Events and Probability. - 3. Random Variables and Their Distributions. - 4. Conditional Probability and Independence. - 5. Solving Elementary Problems. - 6. Counting and Probability. - 7. Concrete Probability Spaces. - Illustration 1. A Simple Model in Genetics: Mendel's Law and HardyWeinberg's Theorem. - Illustration 2. The Art of Counting: The Ballot Problem and the Reflection Principle. - Illustration 3. Bertrand's Paradox. - 2 Discrete Probability. - 1. Discrete Random Elements. - 2. Variance and Chebyshev's Inequality. - 3. Generating Functions. - Illustration 4. An Introduction to Population Theory: GaltonWatson's Branching Process. - Illustration 5. Shannon's Source Coding Theorem: An Introduction to Information Theory. - 3 Probability Densities. - I. Expectation of Random Variables with a Density. - 2. Expectation of Functionals of Random Vectors. - 3. Independence. - 4. Random Variables That Are Not Discrete and Do Not Have a pd. - Illustration 6. Buffon's Needle: A Problem in Random Geometry. - 4 Gauss and Poisson. - 1. Smooth Change of Variables. - 2. Gaussian Vectors. - 3. Poisson Processes. - 4. Gaussian Stochastic Processes. - Illustration 7. An Introduction to Bayesian Decision Theory: Tests of Gaussian Hypotheses. - 5 Convergences. - 1. Almost-Sure Convergence. - 2. Convergence in Law. - 3. The Hierarchy of Convergences. - Illustration 8. A Statistical Procedure: The Chi-Square Test. - Illustration 9. Introduction to Signal Theory: Filtering. - Additional Exercises. - Solutions to Additional Exercises. Language: English