Can I ignore importance, adjoint equations, GRDFs for my path tracer? I need to write a photo-realistic renderer. I have been looking at ScratchAPixel site, asking a couple of questions here on CG, and going through the Advanced Global Illumination 2nd ed book. I've read about radiometry, probability, Monte Carlo, and a bit on Russian roulette. I'm aware of the rendering equation in its hemispherical and area formulations. I've written a SAH based kd-tree, so am ok for efficient ray casting.

I'm poised to start writing some code alongside reading chapter 5 of my book which is about path tracing algorithms. However, the last half of chapter 4 is taken up with talking about the following concepts:


The Importance Function
The Measurement Equation
Adjoint equations and linear transport operators
GRDF (Global Reflectance Distribution Function)


These concepts I've not seen appearing elsewhere in my research (if you can call reading a few web pages about GI rendering proper research?). My question is, do I really need to know this stuff to progress to writing my path tracer? I suspect the answer might depend on which type of path tracer I'm going to developer. To start, based upon what little I know, I think it'll be unidirectional.
No, you don't need to know this stuff to implement basic path tracer.

Basic unidirectional path tracer is quite simple to implement. Just trace bunch of paths of length X for each pixel with uniform distribution over the normal oriented hemisphere at the path's intersection points. Then weight the remaining path with the BRDF at each intersection point and multiply with luminance of light once the path hits a light.

You'll get quite a noisy (but unbiased!) image even for large number of paths and then you can start to look into methods to reduce noise, e.g. importance sampling &amp; bidirectional path tracing. Just validate the more optimized path tracers towards earlier validated path tracers to avoid introducing accidental bias.