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The Variational Calculus with Engineering Applications was and is being taught to fourth-year engineering students, in the Faculty of Applied Sciences, Mathematics – Informatics Department, from the University Politehnica of Bucharest, by Prof. Emeritus Dr. Constantin Udriste. Certain topics are taught at other faculties of our university, especially as master’s or doctoral courses, being present in the papers that can be published in journals now categorized as “ISI”. The chapters were structured according to the importance, accessibility, and impact of the theoretical notions able to outline a future specialist based on mathematical optimization tools. The probing and intermediate variants lasted for a number of sixteen years, leading to the selection of the most important manageable notions and reaching maturity through this variant that we decided to publish at Wiley. Now the topics of the book include seven chapters: Extrema of Differentiable Functionals; Variational Principles; Optimal Models Based on Energies; Variational Integrators; Miscellaneous Topics; Extremals with Nonholonomic Constraints; Problems: Free and Constrained Extremals. To cover modern problem-solving methods, each chapter includes Maple application topics. The scientific authority we have as professors in technical university has allowed us to impose our point of view on the subject and on the types of reasoning that deserve to be offered to readers of variational calculus texts. Everything has been structured for the benefit of functional optimization that describes significant physical or engineering phenomena. To unlock the students’ minds we preferred a simplified language, specific to applied mathematics, sending readers of pure mathematics to the bibliography. Long experience as mathematics teachers in technical universities has prepared us to fluently expose ideas undressed by excessive formalizations, with great impact on the students’ understanding of the natural phenomena encountered in engineering and economics as well as their dressing in mathematical clothing. In this sense, we preferred mathematical modeling as a scientific support for intelligent presentation of the realworld and we avoided the hint of abstract notions specific to pure mathematics.