There is no single "assembly language". Every processor type has a different internal architecture and instruction set. Different operating environments have different tools for converting human readable code ("assembly language") into executable binary code ("machine language").
Pick a processor and an operating environment, then learn the instruction set for that processor, plus how to use the assembler, linker, burner, debugger, whatever for the operating environment. If you want to learn, though, that takes doing...and that takes access to a platform where you can develop, run and debug code for that processor.
It takes a few iterations of this, I think, to "get" what's common to assembly language programming; in spite of differences in CPUs and tools.
AVR is a family of microcontrollers. These ARE processors, designed more for software-control of devices that for building general-purpose computer systems, but the line is a fuzzy one. It is a different architecture and instruction set from the ARM, MIPS, x86, PIC, PowerPC, ...
It's probably easiest to start with assembly for an Intel x86 desktop/notebook running Linux or FreeBSD either directly or using a VM like VirtualBox to run that under WIndows or OSX. The Unix-style assemblers are ugly, especially for x86, but there is a lot of material available in book and on the web.