Élie Cartan's paper "Les groupes réels simples, finis et continus" of 1914

The paper and its progeny are discussed at length in Helgason (1978, p. 537):

In his paper [2] Cartan classifies the simple Lie algebras over R. His method, which required formidable computations, used the signature of the Killing form although it often happens that two nonisomorphic real forms of the same complex algebra have the same signature. Cartan's statement ([2], p. 263): “Les groupes réels d'ordre $r$ qui correspondent à une même type complexe d’ordre $r$ se classent en général complètement d’après leur caractère,” is therefore not to be taken literally; cf. Lardy ([1], p. 195). After noticing the equivalence of problems B and B' (§1) Cartan (in [12]) simplified his original treatment (see also Lardy [1]). Following his general theory [1] of automorphism of complex simple Lie groups, Gantmacher [2] gave a simplified treatment of the real classification. For further developments of this method see Murakami [3], Wallach [2], and Freudenthal and de Vries [1]. While Gantmacher used a Cartan subalgebra $\mathfrak h$ of $\mathfrak g$ whose “toral part” $\mathfrak h\cap\mathfrak k$ is maximal abelian in $\mathfrak k$, Araki develops in [1] a new method using a Cartan subalgebra $\mathfrak h\subset\mathfrak g$ whose “vector part” $\mathfrak h\cap\mathfrak p$ is maximal abelian in $\mathfrak p$. In addition to a solution to problem B' (§1) this method gives valuable information about the restricted roots and their multiplicities (cf. Exercises F). A modification is given by Sugiura [2]. In the present work we use the method of Kac [1] which at the same time gives a rather explicit description of the automorphism $\sigma$ of finite order.

The paper of Cartan is discussed in

D. W. Morris, Introduction to arithmetic groups. Deductive Press, [place of publication not identified], 2015.

The free book can be downloaded from arXiv: https://arxiv.org/abs/math/0106063.

Here is a quote from that book:

The classification of real simple Lie algebras (Theorem 18.1.7) was obtained by E. Cartan [4]. (The intervening decades have led to enormous simplifications in the proof.)