1.Introduction
2.Main definitions and notations
3.Filtering and smoothing recursions
4.Advanced topics in smoothing
5.Applications of smoothing
6.Monte carlo methods
7.Sequential monte carlo methods
8.Advanced topics in sequential monte carlo
9.Analysis of aequential monte carlo methods
10.maximum likelihood inference. Part I (Optimization through exact smoothing)
11.maximum likelihood inference. Part II (Monte carlon optimization)
12.Satistical properties of the maximum likelihood estimator
13.Fully bayesian approaches
14.Elements of markof cain theory
15.An information-theoric perspective onorder estimation
Appendix A. Conditioning
Appendix B.Linear perdication
Appendix C.Notations