Original: It was nominally created in 1672 when Frederick William III, the last duke of Saxe-Altenburg, died and Ernest I, Duke of Saxe-Gotha (who had married Frederick William's cousin, Elisabeth Sophie), inherited the major part of his possessions.
Simplified: It was formed in 1672 when Frederick Wilhelm III, the last duke of Saxe-Altenburg died and Ernest I, Duke of Saxe-Gotha (who had married Frederick Wilhelm's cousin, Elisabeth Sophie) inherited his possessions.