When Edgar died in 1107, he wanted Alexander to succeed him. He also wanted their younger brother, David, to have something of his own, so David was given an appanage. An appanage (from Latin adpanare, literally "to give bread") was traditionally a grant of land for a younger son who normally would not be in the line of succession because of primogeniture. David was given an appanage in southern Scotland, the former kingdom of Strathclyde. This was supported by Henry I of England, the boys' brother-in-law through marriage to their sister Edith, now called Matilda.
Another matrimonial link between the two countries took place when Alexander married Sybilla of Normandy. She was the first child of Henry I with his mistress, Lady Sybilla Corbet. We don't know when they married, but Sybilla was born c.1092, and they were married by 1114 when she was 22. In 1114 Alexander joined Henry on campaign in Wales against Gruffudd ap Cynan of Gwynedd.
Alexander and Sybilla seemed to be a devoted couple, but childless. She died in 1122 while at the village of Kenmore, and Alexander planned an Augustinian Priory at the location. He did not remarry.
Alexander later gained the nickname "the Fierce" because of his short temper with his subjects, but that temper supposedly was never aimed at clergy. He was considered very pious, like his wife. He was the senior lay person in 1104 when the remains of St. Cuthbert were examined before their re-interment, when Ralph d'Escures declared that the saint's body was uncorrupted. He founded religious institutions at Scone and Inchcolm, and had towers built at Dunfermline Abbey where his mother was buried.
His fierceness was earned when he was attacked by men from Moray, where the family of Macbeth ruled who had been his family's enemy not too long before. He pushed them and soundly defeated them.
Alexander died in April 1124, leaving the kingdom to David, who ruled for nearly 30 years and made so many changes that scholars refer to the Davidian Revolution. I'll explain just what changes he made next time.