Experts, please explain in neat manner (tabular or any comfortable way u want):
What is circumcentre, orthocentre, incentre and centroid? What are their properties and how can they be constructed and their specific properties! Please!

Centroid is the point where all the medians meet

and circumcentre is the centre of the circle drawn to  circumscribe  a given figure.

Example :

In the given figure AD, BE and CF are the medians of ΔABC and G is its centroid

and O is the circumcentre of ΔPQR.

The incentre is the point of intersection of the angle bisectors of the triangle.

Here point D is the incentre of triangle.

Orthocentre
 

The altitudes , perpendiculars from the vertices to the opposite sides of a triangle meet at a point- ORTHOCENTRE