Following the tradition of the journal Thermal Science, to collect on one place, and to present to the readers, papers written by eminent experts devoted to the specific modern topic, we have in this issue, in Part one, eleven papers presenting and testing capabilities of the recently developed Analytical methods in non-linear heat transfer and diffusion. This time, again, papers in Part one have been chosen and collected by professors Jordan Hristov and Mohammed El Ganaoui. They also wrote informative and nice preface, giving insight in capabilities of presented analytical methods. I am deeply grateful to the Guest editors, Prof. Jordan Hristov (Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria) and Prof. Mohammed El Ganaoui (Longwy University Technology Institute, University of Lorraine, Nancy, France), for their permanent contributions to improvement of the journal Thermal Science.