What is the difference between Fourier series and Fourier transformation?
The Fourier series is used to represent a periodic function by a discrete sum of complex exponentials, while the Fourier transform is then used to represent a general, nonperiodic function by a continuous superposition or integral of complex exponentials. The Fourier transform can be viewed as the limit of the Fourier series of a function with the period approaches to infinity, so the limits of integration change from one period to $(-\infty,\infty)$.
In a classical approach it would not be possible to use the Fourier transform for a periodic function which cannot be in $\mathbb{L}_1(-\infty,\infty)$. The use of generalized functions, however, frees us of that restriction and makes it possible to look at the Fourier transform of a periodic function. It can be shown that the Fourier series coefficients of a periodic function are sampled values of the Fourier transform of one period of the function.
Fourier transform and Fourier series are two manifestations of a similar idea, namely, to write general functions as "superpositions" (whether integrals or sums) of some special class of functions. Exponentials $x\rightarrow e^{itx}$ (or, equivalently, expressing the same thing in sines and cosines via Euler's identity $e^{iy}=\cos y+i\sin y$) have the virtue that they are eigenfunctions for differentiation, that is, differentiation just multiplies them: ${d\over dx}e^{itx}=it\cdot e^{itx}$. This makes exponentials very convenient for solving differential equations, for example.
A periodic function provably can be expressed as a "discrete" superposition of exponentials, that is, a sum. A non-periodic, but decaying, function does not admit an expression as discrete superposition of exponentials, but only a continuous superposition, namely, the integral that shows up in Fourier inversion for Fourier transforms.
In both case, there are several technical points that must be addressed, somewhat different in the two situations, but the issues are very similar in spirit.
Fourier transform is used to transform periodic and non-periodic signals from time domain to frequency domain. It can also transform Fourier series into the frequency domain, as Fourier series is nothing but a simplified form of time domain periodic function.
Fourier series
Periodic function => converts into a discrete exponential or sine and cosine function.
Non-periodic function => not applicable
Fourier transform
Periodic function => converts its Fourier series in the frequency domain.
non-Periodic function => converts it into continuous frequency domain.