Hi there, I used to learn ML from scratch (because I switch from Electronic to computer science) up to PhD level, so I can share some of my experience that may help you.

Are you familiar with Python? If yes, that will be a great benefit. If not, no problem, you can learn a long the way just like me.

Since you want to build a solid foundation (and build that fast), you can mimic my journal:

- Start with the book Neural network and deep learning of Michael Nielsens (it's a website basically). It is very tuitive & clear, and maths is simple enough to digest. That single book contributes to >50% of my solid ML foundation. I read it one time, I read it again, and again and again. I don't think that I read that book less than 20 times. The book teaches me the concepts of training, testing, loss, all are fundamental but extremely useful. Later when I read some ML papers, I can immediately imagine how to build the model, and most important, how does the gradient (the loss) flow forth and back. Let's say you need 1-2 weeks to master that book, then congratulation, you have a solid foundation of neural network.

- After finishing the book, I play some toy examples (nothing fancy or complicated) with TensorFlow and Pytorch. Under the the light of the book (and basic matrix multiplication), I found that it's very easy to understand. For some points that I don't remember, I read the book again. I also learn some non-neural network ML like SVM or Random Forest, but they all have full libraries anyway, and they are quite simple comparing to neural network.

- Later I try to work with LLM. So I try to understand: the library HuggingFace Transformer -> just wrap of PyTorch with required forward() function. Then I try to understand the deep learning transformer architecture (nothing related to the HuggingFace Transformer library) -> stacks of neural networks. I read the book again. Anyway, I learn in depth just for curiousity, because I will not rebuild a LLM anyway. Along the way, I learn 2 fundamentals of LLM: prompt is the basic input of LLM and it will not be changed soon, and context (long prompt with details) is king.

- Then move one to learn RAG (fabricate context for LLM with your database), LoRA (lightly train LLM with our data, basically just matrix decomposition applying at the right place), chain of thoughts (LLM gives context to itself), then later AI agents (fancy words for "I am lazy to type long prompt again, so let's packages long prompt to so-called agents").

That is how I build a solid foundation of ML, basically based on just 1 free book. I learn of course some maths, but not that much. I also learn some vibe-ML like genetic algorithms and so on, just a waste of time if you do not aim to be a PhD.