Grieg was born in Bergen, and was of partial Scottish descent; the original family name was spelled "Greig". After the Battle of Culloden in 1746, his great-grandfather traveled widely, settling in Norway around 1770, and establishing business interests in Bergen. Edvard was brought up in a musical home. His mother, Gesine, became his first piano teacher.

In the summer of 1858, Grieg met the legendary Norwegian violinist Ole Bull, who was a friend of the family, and whose brother was married to Grieg's aunt. Bull noticed the 15-year-old boy's talent and persuaded his parents to send him to further develop his talents at the Leipzig Conservatory, then directed by Ignaz Moscheles.

Grieg enrolled in the conservatory, concentrating on the piano, and enjoyed the numerous concerts and recitals given in Leipzig. He disliked the discipline of the conservatory course of study, yet he still achieved very good grades in most areas, the exception being the organ, which was mandatory for piano students, at the time. In the spring of 1860, he survived a life-threatening lung disease. The following year he made his debut as a concert pianist, in Karlshamn, Sweden. In 1862, he finished his studies in Leipzig, and held his first concert in his hometown of Bergen, where his programme included Beethoven's Pathétique sonata. (Grieg's own recording of his Piano Sonata, made late in his life, shows he was an excellent pianist).

In 1863, Grieg went to Copenhagen, Denmark, and stayed there for three years. He met the Danish composers J. P. E. Hartman, and Niels Gade. He also met his fellow Norwegian composer Rikard Nordraak (composer of the Norwegian national anthem), who became a close friend and source of great inspiration. Nordraak died shortly after, and Grieg composed a funeral march in his honor. Grieg had close ties with the Bergen Philharmonic Orchestra (Harmonien) and was Music Director of the orchestra from 1880-1882.

On June 11, 1867, Grieg married his first cousin, Nina Hagerup. The next year their only child, Alexandra, was born. The following summer, Grieg wrote his Piano Concerto in A minor while on holiday in Denmark. Edmund Neupert gave the concerto its premiere performance on April 3, 1869 in the Casino Theater in Copenhagen. Grieg himself was unable to be there due to commitments conducting in Christiania (as Oslo was then named).

In 1868, Franz Liszt, who had up to that time had not met Grieg, wrote a testimonial for him to the Norwegian Ministry of Education, which led to Grieg obtaining a travel grant. The two finally met in Rome in 1870. On Grieg's first visit, the two went over Grieg's Violin Sonata No. 1, which pleased Liszt greatly. On the second visit, in April, Grieg brought with him the manuscript of his Piano Concerto, which Liszt proceeded to play by sight (including the orchestral arrangement). Liszt's rendition, greatly impressing his audience, although Grieg gently pointed out to him that he played the first movement too quickly. Liszt also gave Grieg some advice on orchestration, (e.g. to give the slow movement melody to a solo trumpet).

In the summer of 1869, Grieg's daughter Alexandra became ill and died, at the age of 13 months.

In 1876, Grieg created incidental music for the premiere of Ibsen's play Peer Gynt, at the request of the author. Many of the pieces from this work became very popular in the form of orchestral suites or piano and piano-duet arrangements.

Grieg's later life brought him fame but not wealth. He was eventually awarded a government pension from Norway.

Edvard Grieg died in the autumn of 1907, aged 64, after a long period of illness. The funeral drew thousands out on the streets of his hometown to honor the artist. His and his wife's ashes are entombed in a mountain crypt near his house, Troldhaugen.

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