I need to build an electrical transformer for stepping up/stepping down voltages and currents. One method would be to place the secondary coil INSIDE the primary coil, as in a typical Tesla coil setup. The other method is to put the two coils SIDE BY SIDE in proximity, as is normally done. My question is: which method is more efficient, or is there any difference at all? Thanks!

Sorry, I do not believe there is a engineer that specializing in transformers here.

There is a decent amount of info out on the internet, here are some examples:

http://www.ti.com/lit/ml/slup126/slup126.pdf

http://ecee.colorado.edu/copec/book/...Ch15slides.pdf

Transformers Part 1 - Beginners' Guide to Electronics

Power Transformer & Inductor- Design Principles, Calculation, Software

Do a web search for "electric transformer design", for much more info.