Is there any difference between Bravais lattice and primitive lattice? So far I just had the first lecture in solid state physics...I am still confused if there is any difference between Bravais lattice and primitive lattice?
 A: A Bravais lattice is an infinite periodic array of points - essentially a mathematical construct. It can be characterized by primitive lattice vectors $\vec{a_1}, \vec{a_2}, \vec{a_3}$ such that for any integers $n_1, n_2, n_3$, the lattice vector $\vec{R} = n_1\vec{a_1} + n_2\vec{a_2} + n_3\vec{a_3}$ is a lattice point and each lattice vector can be expressed in such a form.
Physically, you get a crystal when you place an atom (or a group of atoms) at each lattice point. If you're placing a group of atoms (sometimes referred to as a motif), associating points to all atoms gives a non-Bravais lattice because not all atoms are at a position described by the general lattice vector $\vec{R}$. Such a lattice is more commonly known as a lattice with a basis.
It's not clear what you mean by primitive lattice. A primitive unit cell is a volume that contains exactly one lattice point, that when displaced by all possible lattice vectors $\vec{R}$ covers the volume of the entire lattice. For instance, the volume defined the primitive lattice vectors is a primitive unit cell. Another commonly used term is conventional unit cell, which is usually a convenient geometric shape that does not necessarily contain only one lattice point. So a non-Bravais lattice will also have a unit cell that would typically contain more than one atom (depending on the basis).
The terminology is understandably confusing, particularly in the beginning. I strongly recommend the book Solid State Physics, by Ashcroft and Mermin.
A: This can often get confusing as physicists and mathematicians tend to have different definitions for lattices, Bravais lattices, unit cells and so on. In physics, we often use lattice to refer to any periodic [1] packing, while we use Bravais lattice to refer to mathematical lattices, namely [2]: 

A Lattice is an infinite set of points defined by integer sums of a
  set of linearly independent primitive basis vectors.

Now I guess by primitive lattice, you meant primitive unit cells (let me know if otherwise). Unit cells [2]:

A unit cell is the repeated motif which is the elementary building
  block of the periodic crystal.

And a primitive unit cell [2]:

A primitive unit cell for a periodic crystal is a unit cell containing
  only a single lattice point.


[1]: A periodic packing can be thought of as a union of many translates of a lattice.
[2]: Simon, Steven H. The Oxford solid state basics. OUP Oxford, 2013.
A: Bravais lattices are those that fill the whole space without any gaps or overlapping, by simply repeating the unit cell periodically. The whole lattice can be generated starting from one point by operating the translation vector
$$\vec{R}\ =\ n_1 {\bf{a_1}}\ +\ n_2 {\bf{a_2}}\ +\ n_3{\bf{a_3}} $$
where $(n_1,n_2,n_3)$ are integers and $({\bf{a_1}},{\bf{a_2}},{\bf{a_3}})$ are the basis vectors which span the lattice.
In three dimensions, there are exactly 14 types of Bravais lattices. A primitive lattice is one such example. A primitive lattice is generated by repeating a primitive unit cell, which contains a single lattice point. 
An example of a primitve unit cell in three dimension would be a cube with lattice points only at the vertices. Now, each of these lattice points is shared by 8 unit cells (4 above, 4 below). So, in each unit cell, one lattice point is counted as $\frac{1}{8}$. Thus, the total no. of lattice points in each unit cell is $\frac{1}{8}\times 8\ =\ 1$
