This issue of the journal Thermal Science continues a special collection of articles devoted to Goodman Heat balance Integral method (HBIM), done by Guest-editor Prof. dr. Jordan Hristov. This is third time that Prof. Jordan Hristov makes special contribution to the quality of the journal thermal Science, by proposing and realization of the brilliant ideas to summarize world' accumulated experience in specific, very important scientific topics. The first time it was in Vol. 10, No. 1, 2006 dedicated to the scientific contribution of Prof. Adrian Bejan, and his influence on many researchers to optimize engineering systems using basic principles of thermodynamics, in particular entropy generation minimization. The second time it was Vol. 11, No. 2, 2007, dedicated to the fundamental aspects of the complex processes during fires. Success of those two issues has been evident on our site. Accordingly, I have accepted with the enthusiasm new brilliant idea of Prof. Hristov to prepare a special issue of our journal dedicated to the 50th anniversary of the Goodman's Heat balance Integral method (HBIM). The result of his hard work and the contributions of the eleven recognized authors you can see in Part I of this issue.