I am learning the Lagrangian formalism from Landau & Lifshitz but I'm not very familiar with variational calculus. Landau assumes its knowledge and uses it directly. Although the equations look analogous to what you'd do with ordinary calculus, I'd like to understand the foundation and ideas behind variational calculus before I continue with Landau's book. I am looking for a book on the Calculus of Variation and have searched this forum a bit. I have boiled it down to Gelfand & Fomin and Lanczos. I want to work towards a strong mathematical foundation to continue with Landau's treatment of the principle of least action. Which one would you recommend? Also, any good video lectures on the topic?