Introduction to (construction) of bases.

Hello everyone. I would like to start reading about

1.orthonormal bases and

2. bases functions

My intention is first to understand what are these two topics about (I recall some lectures since my bachelor studies.. but it would be great to understand them more in depth) and then to try to understand how descriptive some basis-expansion coefficients can be.

Of course it is not very easy for you to give me one link that will contain everything.. but few links might be a good starting point for me. I already googled but I would prefer to have some links for people that have studies this topic before.

I would like to thank you in advance for your help.

Best Regards

Alex