It's a very good question, it's quite confusing, but slightly different about HOW TO USE!
Honestly, the answers above are not perfectly correct.
For example...
○ 私は、最近運動していない(I haven't exercised these days)
× 私は、この間(この前)運動していない
「最近」 indicates term near from now, so it's not just one point of the past.
"haven't exercised" is not the point of the past, but (long) term, so, you must use 「最近」!
「この間」「この前」 are wrong!
○ 私はこの間、すし屋に行きました。(I went to Sushi restaurant recently)
△ 私は最近、すし屋に行きました。
SO, about this sentence, it indicates just one point of the past, so you should use 「この間」or「この前」.
But, 「最近」 is also OK, though native Japanese don't use so much,
because it is for "term" as I explained. But it's also OK, 「最近」 is convenient word^^
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The difference between 「この間」and「この前」 is not so clear, compared with 「最近」,
so if you are beginner, you don't have to care about it.
Native Japanese sometimes use 「この間」 in formal situation (but not so good),
but don't use 「この前」 in formal.
In formal situation, 「先日(せんじつ)」 is the best choice.
About formality, please see this one!
先日>この間>この前>こないだ
I hope I could help you!