a.out replaced by ELF file format?

As I recall, one of the original problems with a.out format is that it only supported three sections: text, data, and bss. ELF allows any number (or at least many more). The a.out header format was very simple, something like:

word <magic>
word <text size>
word <data size>
word <bss size>

The ELF format, in contrast, has section headers, with names, sizes, etc.

Having more sections allows for the standard sections, but also gives us const sections, constructor sections, and even one section per function, if we want it.

The a.out format forced shared libraries to occupy a fixed place in memory. If you wanted to distribute an a.out shared library, you had to register its address space. This was good for performance but it didn't scale at all. See for yourself how tricky it was (linuxjournal).

By contrast, in ELF, shared libraries can be loaded anywhere in memory, and can even appear to be at different addresses to different applications running on the same computer (with the code still effectively loaded in only one place in physical memory)! In order to achieve this, in the IA-32 architecture, a register (%ebx) has to be sacrificed. A more comprehensive reference showing that shared libraries got more complicated in ELF, but that was compiler-side complexity, as opposed to programmer-side.