The last two decades have witnessed an enormous amount of activity related to the construction, analysis and implementation of modern algorithms for the approximate solution of nonlinear conservation laws and related problems. The impact of this activity has been felt in various branches of applied Sciences, from Aeronautics to oil exploration, image processing and beyond. New applications continue to develop.

SIAM Journal of Numerical Analysis (SINUM) is a main outlet for the leading publications in this field. Ami Harten, who served on SINUM Editorial Board until his untimely death in 1994, was a leading figure in this activity. This special SINUM issue is dedicated to him.

Amiram Harten was born in Italy in 1946, while his parents were on their immigrating to Israel, where they finally arrived the following year, 1947. He died near Tel-Aviv on August 5, 1994, from a sudden heart failure.

For most of his career, Ami Harten was associated with Tel-Aviv University (TAU). After receiving his M.Sc. degree from TAU under the guidance of Gideon Zwas in 1971, he continued his graduate studies in Courant Institute, where in 1974 he was awarded his PhD, under the guidance of Peter Lax. After three years as a research scientist at the Courant Institute, he joined the School of Mathematical Sciences of TAU.

Ami Harten was best known for his innovative contributions to the construction and analysis of modern shock-capturing methods for nonlinear hyperbolic conservation laws. Here, lack of smoothness, particularly, spontaneous evolution of discontinuities of various types, is a dominant phenomenon which challenges highly accurate computations. Ami's ideas helped revolutionize modern large scale computations by achieving high-resolution while removing spurious oscillations which are inherent in regions with steep gradients. The concepts of Artificial Compression Method (ACM), Total-Variation Diminishing (TVD) schemes, Uniformly and Essentially Non-oscillatory (UNO & ENO) schemes, are but few of the icons in this field that originated in Ami's works. His invited 1990 ICM address was just one sign of recognition of his leading role.

Yet, it would be incomplete to write about Ami's research without mentioning his unique style and personality. Ami had an extreme interest in his work. Once ignited, he would embark on an intense period of research leading to refreshingly original innovations that addressed the essence of the problem. His research would culminate with constructive algorithms that actually work. He was blessed with critical judgment, and with a warm heart. Conversations with Ami were always laced with loud laughs and a lively but friendly atmosphere that grew around him. Peter Lax writes: "...It is inconceivable... that Ami won't appear, slightly larger than life, and louder, too, full of ideas, ready for a marathon session'.

We used to talk for hours, Ami and I. Ami would start with 'Eitan my friend' to which I replied 'Mon Ami'; and there we went. In these talks Ami kept emphasizing how important the impact of his works was to him. Viewed by many as one of the most influential researchers in this field, it is appropriate that this special SINUM issue on Approximate Solution of Nonlinear Conservation Laws and Related Equations be dedicated to Ami Harten and the impact of his work.

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