871. "Great Heathen Army" invades Wessex
Battles of Reading, Ashdown, Basing, Meretun
The Anglo-Saxon Chronicle describes this invasion in much more detail than the attacks on Mercia or Northumbria, which shows quite clearly its origins as a West Saxon document. The army came first to Reading, and three days later two Danish earls rode farther inland, where they were met by Ealdorman Æthelwulf at Englefield, and one of the Danes was killed. Four days after that King Æthelred and Alfred led a great army to Reading and there was a pitched battle with great slaughter in which Ealdorman Æthelwulf was killed, and the Vikings were victorious.
Four days after that, Æthelred and Alfred had rallied their troops and fought against the Vikings at Ashdown: this fight continued until nightfall and this time the English put the Vikings to flight. The chronicler adds that the Vikings forces were in two halves: King Æthelred faced the one led by the heathen kings, Bagsecg and Halfdan, and Bagsecg was slain, and Alfred faced the one led by the earls, several of whom (Sidroc the Old, Sidroc the Younger, Osbearn, Fræna and Harold) were slain.
A fortnight later Æthelred and Alfred fought the Vikings at Basing, and this time the Vikings won.
Two months later Æthelred and Alfred fought the Vikings at Meretun (unidentified), and the Vikings won, though only after a long battle and great slaughter; the chronicler notes that the English put the Vikings to flight and were victorious far into the day.
871. "Great Summer Army" comes to Reading
The Anglo-Saxon Chronicle puts this arrival in 871, before Æthelred's death in April. The "Great Summer Army" came to Reading, and presumably joined there the "Great Heathen Army" of 865, which had successfully beaten off an English attack on its camp at Reading earlier in the year. The armies probably campaigned together until 874, when Halfdan (the surviving king from the "Great Heathen Army" noted at the Battle of Ashdown in 871) led part of the army up to Northumbria.
late April, 871. Æthelred of Wessex dies
Alfred, Æthelred's brother, succeeds to Wessex
The Anglo-Saxon Chronicle notes that Æthelred died after Easter (April 15 in 871). John of Worcester in his 12th-century chronicle gives the date as April 23, but Stevenson points out that this cannot be trusted, since another and a more famous King Æthelred died on April 23 (1016), and the 12th-century chronicler may have found that date in a calendar, without a year or an identification of which King Æthelred was meant (in the form "9 kal. May [23 April]: rex Æthelredus obiit") and applied it to the wrong king (Stevenson, pp.240-1).
W. Stevenson, ed., Asser's Life of King Alfred together with the Annals of Saint Neots Erroneously Ascribed to Asser (Oxford: 1904)
871. Alfred fights the Vikings at Wilton, and elsewhere
The West Saxons make peace with the Vikings
A month after his accession (so presumably in late May, 871), Alfred led a small force against the Viking army at Wilton, and the Vikings won (though, as in the discussion of the battle at Meretun in 870/1, the Anglo-Saxon Chronicle puts a brave face on it, saying that the English were victorious far into the day, though the Danes won in the end).
Summing up the year 871, the chronicler notes that there were nine large battles (variant figures range from eight to fifteen) against the Danes that year, not counting smaller engagements, that nine Danish earls and one king (Bagsecg, at the Battle of Ashdown) were killed, and only after this does he admit that the West Saxons "made peace" with the Vikings.