Self induction in transformer Wont self induction ruin the working of a transformer ?
While increasing voltage (AC) in the primary coil, wont there happen a self induction in the primary coil itself ?
$E_0 = -L \frac{dI}{dt} $ 
If there happens a change in current it should cause an emf. Even if the inductance is small. There happens a back emf in the coil.
 A: The self-inductance of a transformer is the net inductive effect reflected
onto the primary circuit by the transformer windings. Both the primary and
secondary windings of a real transformer exhibit electrical resistance due to
copper losses, and inductance due to magnetic flux leakage. Although most of
the magnetic flux is confined to the core of the transformer, some flux links
one winding without linking the other (leakage flux). The effect can be
modeled as primary impedance and secondary impedance 'transposed' to the
primary side of an 'ideal' transformer, along with the mutual inductance
(magnetisation) and core losses (typically due to eddy currents and
hysteresis).

The net effect on the current-voltage relationship through a transformer due to
leakage flux is represented by a 'self-inductance'. In large power
transformers, the winding resistance is generally large compared with the
self-inductance, although the value of self inductance is generally not large
compared to the mutual inductance, particularly at full load. When lightly
loaded (<50%) the self inductance can have a noticeable effect in terms of
a 'lag' between the applied voltage and the resulting current. This can be seen
as 'undesirable' from an economic point of view, since it results in a low
'power factor'. This effectively means the full rating of the electrical
transformer and related equipment (wires, switches, etc) are not being
utilitized to their maximum capacity for transferring 'real' power, so there
is some loss in efficiency.
On the other hand, the effect of self-inductance reduces the prospective fault
currents. These are the potentially large electric current which flows when
there is a fault, such as a short circuit between the line and earth ground.
This reduces the need for large 'oversized' cables to handle a high fault
current and also reduces the risk of possible damage caused by such currents.

A: Forget for a moment the secondary coil. Then you do indeed get an EMF as you describe. This is called an inductor, and it's hallmark is that current and voltage are out of phase by 90 degrees, i.e. the voltage drop across the inductor is $L \frac{dI}{dt}$. This does not ruin the transformer, as you say, because it merely means that if the voltage across the transformer is $V_0 \cos\omega t$ then the current is $I = \frac{V_0}{L} \sin\omega t$.
I should clarify something about inductors, that was hinted at in theo's comment. Consider an inductor that is placed in parallel with a perfectly resistive load (a resistor). The fact that current and voltage are out of phase means that current is flowing through the inductor when it is not flowing through the load (because the potential across the load is zero). This component of the current only sloshes back and forth in the inductor, and if the inductor has non-zero resistance, it leads to power loss without any energy making it to the load. In this sense, the self-inductance of the transformer leads to potential efficiency loss but it does not preclude the transformer from working. If the resistance of the primary coils can be lowered or the impedance mismatch be compensated for, then these inefficiencies aren't as important. Often there are bigger losses due to magnetic effects if there are iron cores.
This resource gives a good explanation of how self inductance and mutual inductance go together. I don't have time to put it into the answer right now, but I thought you might find it useful.
