
I went to a top tier school for MechE and Materials, and would recommend two intro books: Engineering Mechanics Statics by Meriam and Kriage and Shigley's Mechanical engineering Design in that order . If you fully understand the contents of these book, it probably puts you in the top 10% of mechanical engineering graduates.
For a broader education, you can read Fundamentals of Heat and Mass transfer by Incropera, DeWitt, Bergmann & Lavine as well as Fundamentals of Fluid Mechanics by Munson, Young & Okiishi.
Understanding these two books will probably as well will probably put you in the top 1% of grads.
If you have a strong background in mathematics, these mostly deal with applications of linear algebra and differentials, so the value is understanding the applications.
From there, you can branch out. If applicable, Ogata's Modern Control Engineering and Tongu's Principles of vibration
Most undergraduates dont really understand these due to the heavy application of Laplace and Fourier transforms, but are relevant if you want to build complex machines.
My initial motivation was to remove configuration. I have found, historically, that giving people options to configure very complex software more often than not results in problems, especially after original developers leave. More often than not these new people will not understand the implications or interactions between various settings and this will just cause problems. So my aim became to remove any options from the software and make sure it can perform autonomously and recover from wide range of, possibly unknown, situations. Which is exactly what control engineering is about if you think about it!
Both are heavy in math, but are not that difficult (I studied theoretical math some 20 years ago and I can read them).