October 26, 1998 Plurisubharmonic functions and potential theory in several complex variables A contribution to the book project D´ eveloppement des math´ ematiques au cours de la seconde moiti´ e du XX e si` ecle Development of mathematics 1950–2000, edited by Jean-Paul Pier Christer O. Kiselman Contents: 1. Introduction 2. Setting the stage 3. The emergence of plurisubharmonic functions 4. Domains of holomorphy and pseudoconvex domains 5. Integration on analytic varieties 6. Weighted estimates for the Cauchy–Riemann operator 7. Small sets: pluripolar sets and negligible sets 8. The analogy with convexity 9. Lelong numbers 10. The growth at infinity of entire functions 11. The existence of a tangent cone 12. The complex Monge–Amp` ere operator 13. The global extremal function 14. The relative extremal function 15. Green functions 16. Plurisubharmonic functions as lower envelopes References Resumo: Plursubharmonaj funkcioj kaj potenciala teorio en pluraj kompleksaj variabloj Ni prezentos superrigardon de la evoluigo de la teorio pri plursubharmonaj funkcioj kaj la potenciala teorio ligita al ili ekde ilia difino en 1942 ˆgis 1997. Abstract: We survey the development of the theory of plurisubharmonic func- tions and the potential theory associated with them from their emergence in 1942 to 1997.