There is a good introductory web-based teaching resource on the reciprocal lattice here: http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/index.php
Reciprocal space is useful because it is the way of thinking about periodic structure (crystals) in terms of the wave vectors of those periodic features. This is necessary if you want to understand the Fourier transform of a crystal which is essential to understand diffraction (elastic scattering) and excitations (the wave-vector dependence of energy, i.e. Brillouin zones etc.). Kittel is a good place to look, after your first steps. http://www.amazon.com/Introduction-Solid-Physics-Charles-Kittel/dp/047141526X
There is a good introductory web-based teaching resource on the reciprocal lattice here: http://www.doitpoms.ac.uk/tlplib/reciprocal_lattice/index.php
Reciprocal space is useful because it is the way of thinking about periodic structure (crystals) in terms of the wave vectors of those periodic features. This is necessary if you want to understand the Fourier transform of a crystal which is essential to understand diffraction (elastic scattering) and excitations (the wave-vector dependence of energy, i.e. Brillouin zones etc.). Kittel is a good place to look, after your first steps. http://www.amazon.com/Introduction-Solid-Physics-Charles-Kittel/dp/047141526X