An English translation of "Die Klassenkörper der Komplexen Multiplikation" was posted on arXiv by CheeWhye Chin in 2020: https://arxiv.org/abs/2006.04531

English translation of the proofs of many theorems from "Die Typen der Multiplikatorenringe elliptischer Funktionenkörper" can be found in

• chapter 14 (eg. Theorem 14.18) of Cox's Primes of the form $x^2+ny^2$ (2nd edition, 2013),
• chapter 13 of Lang's Elliptic Functions (2nd edition, 1987), and
• chapter II (section 4 and 5) of Silverman's Advanced Topics in the Arithmetic of Elliptic Curves (1st edition, 1994).

An English translation of "Die Klassenkörper der Komplexen Multiplikation" was posted on arXiv by CheeWhye Chin in 2020: https://arxiv.org/abs/2006.04531

English translation of the proofs of many theorems from "Die Typen der Multiplikatorenringe elliptischer Funktionenkörper" can be found in

• chapter 14 (eg. Theorem 14.18) of Cox's Primes of the form $x^2+ny^2$ (2nd edition, 2013),
• chapter 13 of Lang's Elliptic Functions (2nd edition, 1987), and
• chapter II (section 4 and 5) of Silverman's Advanced Topics in the Arithmetic of Elliptic Curves (1st edition, 1994).
• Historical discussion about this paper is available in section 8.4 of Roquette's The Riemann Hypothesis in Characteristic p in Historical Perspective (1st edition, 2018)