Original Title: Eventyr, fortalte for Børn, Første Samling, (Første, Andet, & Tredie Hefte)

These were originally published in small, pamphlet-sized volumes. As far as I can tell, from the Hans Christian Andersen Center (which also has all of his stories available to read online), these are the contents of the first collection (Første Samling):

• Vol. 1 (May 1835)
1. The Tinder Box
2. Little Claus and Big Claus
3. The Princess on the Pea
4. Little Ida’s Flowers

• Vol. 2 (Dec. 1835)
1. Thumbelina
2. The Naughty Boy
3. The Traveling Companion

• Vol. 3 (Apr. 1837)
1. The Little Mermaid
2. The Emperor’s New Clothes

He also published Eventyr, fortalte for Børn, Ny Samling (“New collection”) (Første, Andet, & Tredie Hefte) between 1838 & 1841, which contained:

• Vol. 1 (Oct. 1838)
1. The Daisy
2. The Steadfast Tin Soldier
3. The Wild Swans

• Vol. 2 (Oct. 1839)
1. The Garden of Paradise
2. The Flying Trunk
3. The Storks

• Vol. 3 (Dec. 1841)
1. The Rose Elf
2. Ole Lukoie
3. The Swineherd
4. The Buckwheat