Differences between astronomy, astrophysics and cosmology?

What is the main difference between Astronomy, Astrophysics, and Cosmology?

I have the impression that astronomy is a subject that runs parallel to physics but it is outside the physics field. This is based on the division of departments present in many universities: the department of physics being separated from the department of astronomy. The difference between cosmology and astrophysics is more obscure to me. I have the impression, though, that cosmology is more concerned with the structure of spacetime and universe models while astrophysics is more concerned with stellar life cycles, physical properties of stars, galaxies etc.

Which is the field that had more activity/ scientific breakthroughs recently?

In real life, are those classifications even important? Are there many differences between the education process of a future astronomer, astrophysicist or cosmologist?

Somebody, please, give examples of famous astrophysicists, cosmologists and astronomers at the present time.

Answer

Richard Feynman has nice words about science. It is not bad to read chapter 3 of "Feynman Lectures on Physics". The main point of his lecture is that "there is no strict boundary between different fields of science", "nature doesn't concern what we call its parts!"

So, we can't look for a line that divides celestial works into astronomical or astrophysical or cosmological. Although the main keywords about these fields are respectively: "observation of celestial bodies", "machinery of celestial bodies", "evolution of cosmos as a whole". Surely, they use findings of each other.

Recently, cosmology has encountered with big questions, really big! Dark matter and dark energy are the most challenging ones. But it is interesting that if there weren't astronomers and their numerical data, cosmology could not progress.

Usually the students of astronomy focus on classical mechanics and optical methods to be able to observe celestial bodies. Astrophysicists concern general relativity and nuclear physics as two important tools to describe stars or galaxies. But cosmologists are interested in modern theories too, especially string theory. Therefore the courses which they pass should be related to these subjects.