Short course on continuous logic, Notre Dame, June 2016: included here are some historical remarks about continuous model theory

Short course on continuous model theory and operator algebra, Nashville, May, 2017

(MTFMS) The book "Model theory for metric structures" by I. Ben Ya'acov, A. Berenstein, C. W. Henson and A. Usvyatsov

Slides from the special session on continuous model theory, ASL annual meeting, Mar. 2017

Here is a link to a course on continuous model theory I taught a few years ago

Paper by D. Sherman with historical remarks about ultraproducts

Introductory notes on von Neumann algebras for model theorists by I. Goldbring

ICM lecture by Ilijas Farah on Logic and Operator Algebras

(FHLRTVW) Preprint of a book by I. Farah, B. Hart, M. Lupini, L. Robert, A. Tikuisis, A. Vignati and W. Winter on Model theory and C*-algebras

(BCI) Article showing that there are continuum many theories of II_1 factors by R. Boutonnet, I. Chifan and A. Ioana; to appear in Duke

Here is an earlier tutorial (talk1, talk2, talk3) by C. W. Henson at the Max Planck Institute in Bonn on continuous model theory

A tutorial at the 2005 Athens Logic Colloquium by I. Ben Ya'acov - where we came from or how far we've come