How many atoms of aluminum are in 0.1 mol of aluminum?

The number of 'entities' in a mole of any pure substance is always that. 1 mole is equivalent to the number of atoms in a 12g lump of Carbon12.

Edit: I deliberately avoided using Avogadro's number as that is different, in a technical sense, to a mole. A mole is a base unit of the International System of Units (SI) which recognized amount of substance as an independent dimension of measurement. With this recognition, the Avogadro constant was no longer a pure number but a physical quantity associated with a unit of measurement, the reciprocal mole (mol−1) in SI units.  

Therefore Avogadro constant is DERIVED from the mole (nowadays) to give something like 6.02214179 x 10^23 mole^(-1). (based on 2006 evidence)