What is unix? That's a loaded question.
The short answer is ``Unix is an operating system''. So is Gnu/Linux, which is often just called Linux. So are HP/UX, AIX, NeXT STEP (now called Apple Macintosh OS 10), & Microthought Winders (often called many uncomplimentary things).
If this short answer is enough for you, congratulations on knowing the value of keeping things simple. Now skip ahead to Chapter 4 ``Some Basic Commands''.
The long answer is ``It depends on who you ask''.
In my opinion, unix is a description of the function of an operating system. I even say that unix is an Application Programmer's Interface (API). Any operating system which implements the unix API is a unix; it's an implementation of unix. Gnu/Linux is a unix.3.1 Gnu/Linux is often called Linux, but strictly speaking, Linux is a unix kernel, but not a whole unix operating system. There are many other implementations of unix. I can name original BSD, OpenBSD, FreeBSD, NetBSD, HP/UX, AIX, Minix, Apple Macintosh OS 10, NeXT STEP, QNX, & Lynx. There are probably others.
Now for some legal bullshit. ``UNIX'' is a trademark of The Open Group. From what I can infer from their web site about their opinions of what unix is, they would agree with me that it's a description of the function of a family of operating systems, but they would also add ``that we have certified to be UNIX''. So legally, it's not a UNIX unless The Open Group certifies it as a UNIX. So a lot of those operating systems I listed as unices are not UNIXes. It's a thoroughly sad case of legalities getting in the way of simplicity & sanity.
Anyway, I say that if an operating system behaves like unix,
then it's a unix, though not necessarily a UNIX
.
Another opinion, which I don't share, is that Unix is a particular product. HP/UX is another. AIX is another. Gnu/Linux is another. You get the idea.
Fine, except that there is no product simply called ``Unix'' for sale today. You can't even point at a product that is the direct descendant of the original Unix that Ritchie & Thompson wrote at AT&T. Their Unix was the definitive Unix, the original, the one named Unix. You can't buy it today, methinks. And many of those that you can obtain today shared code with the original Unix. BSD is Unix as modified by students at the University of California in Berkeley. That's where sockets were invented. BSD branched into many implementations, several of which are alive & well today. Theoretically, each of those implementations has at least some of the original Unix code in them. Yet somehow BSD isn't a unix? Get real. I'm sure there are similar examples of cross-pollination between the other unix operating systems available today.
Another problem with the claim that BSD, Gnu/Linux, & the others are not unix is that it takes little effort to write a program that runs on all of them. There are enough differences that a non-trivial program requires a little care to be portable, but it's not like portability concerns affect the architecture of your program. All in all, it is easy to port code between HP/UX, AIX, Gnu/Linux, & the BSDs. This isn't an accident. Those products are implementations of a single idea of what an operating system should be. That idea needs a name so that when you ask me what kind of operating system I program for a living, I don't have to reply with ``I'm an HP/UX, Gnu/Linux, AIX, FreeBSD, NetBSD, OpenBSD, QNX, & others programmer''. I say the name for that concept is ``unix''. If not, then it's POSIX, but POSIX is also a trademarked term with a certification schedule from The Open Group (together with IEEE).
So somewhat out of contempt for our legal system's petty concerns for terminology, I say it's all ``unix''. There you have it, in more detail & controversy than anyone with a sense of perspective would ever want.