What do I need to know to learn Lorentz Trans. and theory of relativity?

All that is required to do the math for Special Relativity / Lorentz Transforms, is to be able to square and do square roots. Knowing how to evaluate limits might help, but is not required (usually).

Learn this formula:

gamma = 1 / sqrt( 1 - (v/c)^2 ), a number that is always 1 or greater

Length contraction means a measured length of a moving object is always less than if the object were at rest, so measured_length = rest_length / gamma

Time dilation means a measured duration of events in a moving frame (say two clock ticks) is always less than if the events were in a rest frame, so measured_duration = rest_duration / gamma

You will come across "relativistic mass", in your studies. This is a horrible joke, Do not spend a lot of time on it. The best Energy formula to remember is E^2 = (pc)^2 + (mc^2)^2, with p as a vector (relativistic momentum = gamma * m * v). Relativistic mass considerations use just E = mc^2, and squeeze all the complexity into the m term, meaning a mass with a different scalar value depending on which direction you intend to accelerate it.

The mover and the rest frame both agree on the mover's speed. They will not necessarily agree on the speed of a third relatively moving object / person:

http://www.physics.adelaide.edu.au/~dkoks/Faq/Rela...

Note the above is just the Special (as in Limited) Theory. It obviates consideration of significant mass, acceleration (other than brutally simple), and gravitation. The General Theory covers these, but the math required is introductory material for an advanced mathematics degree. It also does not generate closed form solutions (nice formulas) without significant simplifications.

Best would be to get a good book. I like "Spacetime Physics" by Taylor and Wheeler, but there are other good choices:

http://www.physics.adelaide.edu.au/~dkoks/Faq/Admi...