Cover -- Half-Title Page -- Title Page -- Copyright Page -- Contents -- Introduction -- PART 1: Learning to use Pontryagin's Maximum Principle -- 1. The Classical Calculus of Variations -- 1.1. Introduction: notations -- 1.2. Minimizing a function -- 1.2.1. Minimum of a function of one variable -- 1.2.2. Minimum of a function of two variables -- 1.3. Minimization of a functional: Euler-Lagrange equations -- 1.3.1. The problem -- 1.3.2. The differential of J -- 1.3.3. Examples -- 1.4. Hamilton's equations -- 1.4.1. Hamilton's classical equations -- 1.4.2. The limitations of classical calculus of variations and small steps toward the control theory -- 1.5. Historical and bibliographic observations -- 2. Optimal Control -- 2.1. The vocabulary of optimal control theory -- 2.1.1. Controls and responses -- 2.1.2. Class of regular controls -- 2.1.3. Reachable states -- 2.1.4. Controllability -- 2.1.5. Optimal control -- 2.1.6. Existence of a minimum -- 2.1.7. Optimization and reachable states -- 2.2. Statement of Pontryagin's maximum principle -- 2.2.1. PMP for the "canonical" problem -- 2.2.2. PMP for an integral cost -- 2.2.3. The PMP for the minimum-time problem -- 2.2.4. PMP in fixed terminal time and integral cost -- 2.2.5. PMP for a non-punctual target -- 2.3. PMP without terminal constraint -- 2.3.1. Statement -- 2.3.2. Corollary -- 2.3.3. Dynamic programming and interpretation of the adjoint vector -- 3. Applications -- 3.1. Academic examples (to facilitate understanding) -- 3.1.1. The driver in a hurry -- 3.1.2. Profile of a road -- 3.1.3. Controlling the harmonic oscillator: the swing (problem) -- 3.1.4. The Fuller phenomenon -- 3.2. Regular problems -- 3.2.1. A regular Hamiltonian and the associated shooting method -- 3.2.2. The geodesic problem (seen as a minimum-time problem) -- 3.2.3. Regularization of the problem of the driver in a hurry.