The Azure Damselfly can be distinguised from the similar looking Common Blue Damselfly (Enallagma cyathigerum) by having more black on its back and by having two little black stripes on the side of its thorax.
The Common Blue Damselfly has only one little black stripe on the side of its thorax.

Top: Zanderij Crailo, Hilversum, The Netherlands, 22 June 2013
Left: De Snip, Hilversum, The Netherlands, 18 June 2013
Middle & Right: Botanical Garden, Utrecht, The Netherlands, 7 July 2011