What does an integral symbol with a circle mean? I have frequently seen this symbol used in advanced books in physics:
$$\oint$$
What does the circle over the integral symbol mean? What kind of integral does it denote?
 A: It's an integral over a closed contour (which is topologically a circle). An example from Wikipedia:
$$ \begin{align} \oint_C {1 \over z}\,dz & {} = \int_0^{2\pi} {1 \over e^{it}} \, ie^{it}\,dt = i\int_0^{2\pi} 1 \,dt \\ & {} = \Big[t\Big]_0^{2\pi} i=(2\pi-0)i = 2\pi i, \end{align} .  $$
A: It basically means you are integrating things over a loop. For e.g. a circle with an element $\text{d} \textbf{l}$ if you do $\oint{\text{d} \textbf{l}}$ it will give you circumference of the circle.
A: It's an integral over a closed line (e.g. a circle), see line integral.
In particular, it is used in complex analysis for contour integrals (i.e closed lines on a complex plane), see e.g. example pointed out by Lubos.
Also, it is used in real space, e.g. in electromagnetism, in Faraday's law of induction (part of the Maxwell equations, written in an integral form):
$$\oint_{\partial \Sigma} \mathbf{E} \cdot d\boldsymbol{\ell} = - \int_{\Sigma} \frac{\partial \mathbf{B}}{\partial t} \cdot d\mathbf{A} $$
saying that the generated voltage (an integral of electric field along a circle) is the same as the time derivative of the magnetic flux.
