The dark web is the shady part of internet town, and for those unfamiliar with its .onion alleys it can be hard to know where legal activity ends and illegal activity begins.
Before you consider accessing the dark web, it's a good idea to get up to speed with a few distinctions: namely, the difference between the deep web and the dark web. The deep web generally relates to portions of the internet that aren't crawled by search engines (that includes your online banking and work intranet), while the dark web is a subsection of this that is purposefully hidden by layers of encryption.
So is the dark web safe? Short answer: some of it is, a lot of it isn't.
The dark web, as a concept in itself, is not illegal. Tor, the software used to access the dark web, is not illegal to use. What can be found on the dark web using Tor, however, can be highly illegal. This means you won't be breaking the law by accessing the dark web, but you should be aware that much of what exists on the dark web could get you in a lot of trouble.
“Safe” is a bit of a vague term. There is much of worth to be found on the dark web, but by its nature it is not as safe as the surface-level internet. You can only access pages by having a direct link (normally with a .onion suffix) and while that makes it harder to accidentally stumble across illegal content, you're only a click away from some pretty horrible stuff.