The Sandhi (combination of sounds) of "पुस्तक" (pustak) + "आलये" (aalaye) is पुस्तकालय (pustakalaya). This means "library" in Sanskrit and Hindi.

The combination follows the rules of Sanskrit Sandhi, where the अ (a) at the end of पुस्तक and आ (aa) at the beginning of आलये combine to form आ (aa).

A relevant source explaining Sanskrit Sandhi can be found at: Wikipedia - Sandhi