Reddit mentions of The Statistical Analysis of Failure Time Data

It is a little difficult to answer without more information such as the text you are using for your course, the programming languages you know, and an idea of what you will be doing in your internship. I assume your internship will be doing more applied stuff like writing code to maintain/clean data and run analyses for models that others develop. In that case, I would recommend this book for survival analysis in SAS. If you want more theoretical stuff, then this book is a standard PhD level text.