Common types of adhesives used with aluminum profiles in construction include epoxy resins, which offer strong bonding and resistance to chemicals and temperature changes; polyurethane adhesives, known for their flexibility and durability; silicone adhesives, which are excellent for sealing and bonding in a wide range of temperatures; acrylic adhesives, valued for their versatility and quick setting times; and cyanoacrylate or 'super glue', which bonds quickly and is great for small, precise applications. Each type has unique properties that make it suitable for different construction needs.