Short answers, pulled from the story.
Suetonius Paulinus, the Roman governor of Britannia, led the first invasion of Anglesey in 60 or 61 CE. He built flat-bottomed vessels to cross the Menai Strait with his infantry while his cavalry swam alongside their horses. He was forced to withdraw almost immediately because of the Boudican revolt in southern Britain.
Anglesey was an important centre for the Celtic Druids and their religious practices, making it a place of resistance to Roman rule. The decision to invade may also have been influenced by knowledge of copper mines on the island.
Gnaeus Julius Agricola, governor of Britannia, completed the conquest of Anglesey in 77 CE. He sent auxiliary soldiers recruited in Britain to swim across the Menai Strait without boats, taking the island's defenders by surprise. The island submitted and remained under Roman rule for over three centuries.
The Roman historian Tacitus is the only surviving written source for both invasions of Anglesey. The first invasion appears in his work The Annals, and the second is recorded in The Life of Gnaeus Julius Agricola, written to commemorate his father-in-law. Tacitus may have had access to first-hand accounts from Agricola, who was present at both invasions.
Archaeologists have found a Roman fortlet near Cemlyn Bay, dated by coins from the reigns of Nerva and Hadrian, discovered via aerial photography in 1990. A civilian trading settlement at Tai Cochion with Roman-style corridor housing was active between roughly 100 and 300 CE. Around 18 round copper ingots, eight bearing Roman stamps, have also been recovered from the island.
No major civic centres or villas have been found on Anglesey, and archaeology has revealed little Roman-style building, indicating that Romano-British culture had far less influence there than in other parts of the province of Britannia. Traditional round houses continued to be used alongside any Roman-style structures, and the island was administered from Segontium on the mainland rather than from any urban centre on the island itself.