1. Newton's methods. 1.1. Convergence under Lipschitz conditions. 1.2. Convergence under generalized Lipschitz conditions. 1.3. Convergence without Lipschitz conditions. 1.4. Convex majorants. 1.5. Nondiscrete induction. 1.6. Exercises -- 2. Special conditions for Newton's method. 2.1. [symbol]-convergence. 2.2. Regular smoothness. 2.3. Smale's [symbol]-theory. 2.4. Exercises -- 3. Newton's method on special spaces. 3.1. Lie groups. 3.2. Hilbert space. 3.3. Convergence structure. 3.4. Riemannian manifolds. 3.5. Newton-type method on Riemannian manifolds. 3.6. Traub-type method on Riemannian manifolds. 3.7. Exercises -- 4. Secant method. 4.1. Semi-local convergence. 4.2. Secant-type method and nondiscrete induction. 4.3. Efficient Secant-type method. 4.4. Secant-like method and recurrent functions. 4.5. Directional Secant-type method. 4.6. A unified convergence analysis. 4.7. Exercises -- 5. Gauss-Newton method. 5.1. Regularized Gauss-Newton method. 5.2. Convex composite optimization. 5.3. Proximal Gauss-Newton method. 5.4. Inexact method and majorant conditions. 5.5. Exercises -- 6. Halley's method. 6.1. Semi-local convergence. 6.2. Local convergence. 6.3. Traub-type multipoint method. 6.4. Exercises -- 7. Chebyshev's method. 7.1. Directional methods. 7.2. Chebyshev-Secant methods. 7.3. Majorizing sequences for Chebyshev's method. 7.4. Exercises -- 8. Broyden's method. 8.1. Semi-local convergence. 8.2. Exercises -- 9. Newton-like methods. 9.1. Modified Newton method and multiple zeros. 9.2. Weak convergence conditions. 9.3. Local convergence for Newton-type method. 9.4. Two-step Newton-like method. 9.5. A unifying semi-local convergence. 9.6. High order Traub-type methods. 9.7. Relaxed Newton's method. 9.8. Exercises -- 10. Newton-Tikhonov method for ill-posed problems. 10.1. Newton-Tikhonov method in Hilbert space. 10.2. Two-step Newton-Tikhonov method in Hilbert space. 10.3. Regularization methods. 10.4. Exercises.