The edge is the outermost part or surface of something, or the part that is farthest from the center.
Be careful with that knife. I just bought it, so the edge is extremely sharp. If you touch the tip with your finger, you're bound to cut yourself.
She hasn't lived in the city centre for years. She's actually on the edge of town, at least a 45-minute tube ride away.
To be on edge means to be nervous or anxious about something. On the other hand, to take a lot of risks is to live on the edge.
Larry is really on edge this morning because of his doctor's appointment later. We should only bother him if it's absolutely necessary.
Theresa has only just returned from hiking solo in the Andes and now she's in Laos on one of those dangerous rafting trips. She's really living on the edge these days.
The brink is the edge, especially near a steep slope like the top of a cliff. Most often we use the word figuratively for a negative or serious situation. We usually say on the brink of to describe something (usually negative) that is very likely to happen soon. For example, a nation on the brink of war is probably going to go to war soon.
The elephants are on the brink of extinction because of the ivory trade. Poachers, or criminal hunters, are killing too many of them and selling their ivory tusks.
We use pull back from the brink (of) to describe actions that prevent or lessen a coming disaster.
The Chancellor's reform package helped to pull the economy back from the brink of collapse.
Ewan was drinking and using drugs for several years before his friends pulled him back from the brink by making him go to rehab. Now he is sober and counsels students on healthy living.