Why is a book on a table not an example of Newton's third law? My textbook explains Newton's Third Law like this:

If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A

It then says:

Newton's 3rd law applies in all situations and to all types of force. But the pair of forces are always the same type, eg both gravitational or both electrical.

And:
If you have a book on a table the book is exerted a force on the table (weight due to gravity), and the table reacts with an equal and opposite force. But the force acting on the table is due to gravity (is this the same as a gravitational force?), and the forcing acting from the table to the book is a reaction force. So one is a gravitational, and the other is not. Therefore this is not Newton's Third Law as the forces must be of the same type.
 A: This is common misconception with my students too, and the only way to understand it you must draw all forces that act on both objects (in total five forces)!
In order to make things clearer, I will label the force with which table acts on book as $F_{12}$ and not $F_\text{N}$!  Also suppose that $z$ axis is vertically up, so positive forces push upward and negative forces push downward.  
There are two forces acting on book, its gravitational force $-F_\text{g,book}$ (downward) and the force of table on the book $F_{12}$ (upward).  According to first Newton law for the book they are equal by magnitude
$$F_{12} - F_\text{g,book} = 0.$$
According to the third Newton law book must be acting on table with the force $-F_{12}$ (downward).  So there are three forces acting on table: its gravitational force $-F_\text{g,table}$, force of the book $-F_{12}$ (both downward) and the force of the ground $F_\text{N}$ (upward)!
Now let's write the first Newton's law for the table
$$F_\text{N} - F_{12} - F_\text{g,table} = 0.$$
Consequently
$$F_\text{N} = F_{12} + F_\text{g,table} = F_\text{g,book} + F_\text{g,table}$$
The ground force must support both book and table!  Isn't that obvious?
Conclusion: So third Newton's law is perfectly valid for this case as well!
If you still do not understand, write on the paper book, table, and all five forces (two acting on the book and three acting on the table).
A: One way to make it obvious is think about how the down-momentum is flowing. The book is getting down-momentum from the Earth (through action-at-a-distance gravity), and this down-momentum then flows downwards to the table, and across the table to the legs, then through the legs of the table back down to the Earth, making a closed circuit of down-momentum, like a closed electrical circuit.
Each time momentum leaves an object A and enters another object B, we say a force is acting from A to B, and simultaneously that a reaction force is acting from B to A (since the momentum gained by B is the momentum lost by A). This is Newton's third law.
In this circuit, the down-momentum goes
Earth $\rightarrow$ book $\rightarrow$ table $\rightarrow$ Earth
So there is an action/reaction pair from the Earth to the book (the Earth is pulling the book and transferring down-momentum to it, and the book is pulling the Earth, transferring an equal amount of negative down-momentum--- or up momentum--- to the Earth). There is an action reaction pair from the book to the table ( the book is transferring down-momentum to the table through a contact normal force, and the table is transferring negative down-momentum to the book by the same contact normal force), then the table has an action/reaction pair with the Earth (the table sends the down-momentum into the Earth, and the Earth sends negative down-momentum into the table)
Each of these flows is describing how a conserved quantity, namely down-momentum is going from place to place. It is easiest to sort this out with flows of charge, because unlike charge, momentum is a vector.
A: 
And: If you have a book on a table the book is exerted a force on the table (weight due to gravity),

That's where you went wrong. The force that the book exerts on the table is not a gravitational force, it's a normal force.

and the table reacts with an equal and opposite force.

That's also a normal force. So the book exerts a (normal) force on the table, and the table exerts a (normal) force on the book.

But the force acting on the table is due to gravity (is this the same as a gravitational force?),

No, it's not, and in fact this force (the normal force) is only indirectly due to gravity. The only relevant gravitational force is the force exerted by the Earth on the book. And the book also exerts a gravitational force back on the Earth, but because the Earth is so heavy, that force has no noticeable effect. (The Earth also exerts a gravitational force on the table, and the table on the Earth, but those don't matter so much in this particular scenario.)
A: Newton's third law is about pairs of objects interacting. The force that acts on one object is equal and opposite to the force acting on the other object. So you can never have a third law pair acting on the same object. 
The equality of the reaction force and the weight force is nothing to do with the third law, and is just as a result of the first law applied to the forces acting on the book.
Let's look at some third law pairs in this scenario:


*

*The weight of the book and the weight of the earth. Yup, the earth is pulled up by the book, but because $F=ma$ and the earth is more than a little heavier, it doesn't result in a great deal of movement on the earth's part when the book is released!

*The normal force of the table on the book and the book on the table. The force that the book exerts on the table is a normal force, not a weight force. (The book's weight doesn't act on the table, it acts on the book.) It's equal in magnitude to the weight of the book, again, because of the first law. The book and the table press on each other. It's probably better to think of the normal force as being generated by the electromagnetic forces between molecules in the table and book. You get a normal pair like this in the man-leaning-on-wall example.

*The normal forces between the desk and the earth

*The weight forces between the desk and the earth

*(The gravitational forces between the book and the table are negligable.)


Force 1=Force 2 in magnitude by law 1, not by law 3. (Same for forces 3 and 4.)
A: A lot of questions here talk about "normal force", but I get the feeling that you're still confused about what that is.
First consider the book - Whether it is resting on the table or not, it has a weight. Here weight is different from mass. The weight is the mass $m$ times the acceleration due to Earth's gravity $g$, or more familiarly $$F = mg$$
The same goes for the table. Now this is the important part - The weight isn't gravitational force. The gravitational force that you are thinking of is expressed as $$F_g = \frac{Gm_1 m_2}{r^2}$$ and that is the force due to the gravitational attraction between two bodies.
In the case of the table and the book, the gravitational attraction is absolutely negligible, since they are both so tiny. The force that the table experiences because of the book is what is being called normal force.
The table then exerts an equal and opposite force. This is also clearly seen, because if the table didn't exert an equal and opposite force, the book would be accelerating downward. But the whole system is at rest, therefore the total force on the book-table system must be zero.
EDIT: @AndrewC has mentioned in the comments below why my earlier reasoning was wrong. Basically normal force is only indirectly due to gravity. Khan Academy has a brilliant explanation of these concepts.
A: You need to sort out these ideas. 
1 Free body diagrams:
   Book table
   Book and earth
   Table and earth 
2 sort the force pairs by 'kind' of force:
Interaction is contact (due to electric forces)
Gravity is force due to each of the bodies
So book-table has force pairs due to interaction forces, balanced and oppsite, call them normal due to book, normal due to table. Both same kind. Sorted. 
Book-earth has force pair due to gravity of each acting on other. Both same kind of forces, equal and opposite, and on different bodies 
Table-earth, there is contact, which is electric interaction at electronic charge level. Equal, opposite yet same kind of force. 
Finally, each mass has gravity and the mass exerts force on other mass - NOTE:  "on other mass!!!!" Same kind of force again. 
Conditions for N3:
Equal magnitude
Opposite direction
Same kind of force
