Where can I find a comprehensive derivation of the Euler-Lagrange equation?

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A request for a comprehensive online derivation of the Euler-Lagrange equation from the principle of least action is made. The Wikipedia page on the Euler-Lagrange equation is suggested as a resource. Participants express interest in finding detailed explanations and derivations. The discussion emphasizes the need for thorough and accessible educational materials on this topic. Comprehensive resources are crucial for understanding the mathematical foundations of the equation.
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Can someone link me to a thorough online derivation of the Euler-Lagrange equation from the principle of least action?
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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