For any meaningful research, a fundamental understanding of asymptotic relationships is very important. In our journey towards new algorithms, we compare several algorithms and have to argue using commonly accepted notions, how each of them relate to one another. See this video for a good coverage of the basics where Pratik Shah talks about the O,o,Ω,ω and Θ notations with simple examples.

Having left out the constants, a somewhat imprecise comparison of notations is here:

f(n) = O(g(n)) ≈ f(n) ≤ g(n)

f(n) = Ω(g(n)) ≈ f(n) ≥ g(n)

f(n) = Θ(g(n)) ≈ f(n) = g(n)

f(n) = o(g(n)) ≈ f(n) < g(n)

f(n) = ω(g(n)) ≈ f(n) > g(n)