All papers of this title have been peer-reviewed. The main goal of this series of conferences is to bring together experts and young talented scientists from Bulgaria and abroad to discuss modern trends and to ensure exchange of views in various applications of mathematics in engineering, physics, economics, biology, etc. Keeping the main topics of the previous AMEE conferences as well as the big success of AMEE'07, this year's 34th issue was again subject to the motto 'Nonlinear phenomena - mathematical theory and environmental reality'. The organizing Committee encouraged the participation of senior and postgraduate students and organized a separate youth session. The invited speakers organized two special sessions. Within the 34th Conference AMEE'08 a 'Round Table - Presentations and Discussion - on Mathematics Education in Bachelor Degree Programs and in Master Degree Programs', Conference Tutorial "Introduction to Software Agents and Their Applications', and Workshop on Grid and Scientific Engineering Application (GRID&SEA) took place. The publishing, promotion and distribution the proceedings among the mathematical and related societies taking an interest in its topics is an integral part of the Conference.