This is a revised version of the 1984 book of the same name but considerably modified and enlarged to accommodate the developments in recursive estimation and time series analysis that have occurred over the last quarter century. Also over this time the CAPTAIN Toolbox for recursive estimation and time series analysis has been developed at Lancaster for use in the MatlabTM software environment (see Appendix G). Consequently the present version of the book is able to exploit the many computational routines that are contained in this widely available Toolbox as well as some of the other routines in MatlabTM and its other toolboxes. The book is an introductory one on the topic of recursive estimation and it demonstrates how this approach to estimation in its various forms can be an impressive aid to the modelling of stochastic dynamic systems. It is intended for undergraduate or Masters students who wish to obtain a grounding in this subject; or for practitioners in industry who may have heard of topics dealt with in this book and while they want to know more about them may have been deterred by the rather esoteric nature of some books in this challenging area of study.