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If $\epsilon$ is an alternating unit tensor and $\mu$ is any arbitrary tensor, then what does the

expression $\epsilon : \mu = 0$ mean ? I came across this is some textbook I was reading. Is is tensor product or something else ?

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For matrices this usually means componentwise multiplication. –  Miguel Jan 13 '13 at 17:49
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To expand a bit on my comment:

Two dots in the context of tensors may denote the simultaneous contraction of two indices. Just as with matrices, if $R$ and $S$ are a $(2,0)$ and a $(0,2)$ tensor respectively, then $R:S$ is the scalar $R^{ij} S_{ij}$ (sum over repeated indices).

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