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The earliest beginnings of the Romans arriving in Scotland was in AD 79 when Agricola, the roman leader of Britannica sent a troop to examine Scotland and map its coast. In AD 83 Caledonian groups in Northern Scotland knew they were vulnerable to an invasion by Agricola. The Caledonians starting preparing for this by using guerrilla methods which targets Roman forts and troops.
By 84 AD Agricola had advanced into the Caledonian areas of North-Eastern Scotland. There was an important part of this march where the Caledonians made a mistake when confronting them by doing it head first. Sadly the Caledonians lost the battle against the Roman Army which resulted in 10000 of them dying due to lacking the strong methods, co-operations, and stable structured discipline.
Emperor Domition instructed Agricola to return to Rome in order to fix the military calamity on the egdes of Danube and Rhine.
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The Romans would enter southwards and construct Hadrian's Wall in 122 AD between the estuaries of Solway and Tyne, which led to the creation of the highest northern line of the empire. Hadrian's replacement Antoninus Pius would then contruct the Antonine Wall.
The Antonine wall was constructed to use for the Roman Empire's advocacy and to increase their dividing line. When Antoninus passed away the wall was left behind in support for the Hadrian Wall.
During the era along the fronter, groups on the North of Hadrian's wall would connect to create the Pictish country. Their name become known in 297 AD and originated from the Latin word Picti which means Painted People.
In 306 AD , Emperor Constantius Chlorus had to safeguard his northern border against Pictish assualts towards Hadrian's wall.
As debitilitated the Picts became more confident. This was until 306 AD when the Picts co-operated with the Gael from Ireland, they would begin an invasion on Hadrian's wall. Emperor Julian sent battalians to fight to picts but it did not work out as expected. The Pitchish invasion would extend further down the South.
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The Roman's structure of law and order disintegrated and the Hadrian's wall would be left behind and in 411 AD. The Roman Battalions then withdrew from British Shores in order to handle a crisis within the empire.
Information Source: https://www.historic-uk.com/HistoryUK/HistoryofScotland/Romans-in-Scotland/