Thismonographisintendedasasimpleintroductiontotheso-calledLULU-theory and the practical use of LULU-smoothers leading up to a full Multiresolution Analysis of any ?nite sequence. The attempt has been to present the subject in a way that is retrospectively ordered to some extent, but preserves some of the twisted paths that intuition initially suggested. It is based on the few publications in the subject, some already submitted and lectures given at conferences and on invitation at public and private institutions. The ideas originated more than ?fteen years ago when the author was - volved in practical problems at the Institute for Maritime Technology in Sim- stown and advanced while the author was at the BMI in Stellenbosch. The author hopes that publication of this book will stimulate the interest of other researches and takes responsibility for any remaining typographical or technical errors. A growing love for this particular subject was one of the prime reasons for a return to academic life, and a perceived opportunity to consolidate various p- spectives and results. It is however only the encouragement, guidance and help of severalrespected people that have resulted in the e?ort presented here.