Pretty sure this is Magi-Nation.

Three thousand years ago in the Moonlands, the Shadow Magi Agram was sealed inside the planet's Core by the Core Glyph and the Dreamstones which provided its power. Now he plans to escape by using his Shadow Geysers to weaken his prison in order to bring the Moonlands under his control, and only a Magi known as the "Final Dreamer" can stop him. A young boy from Earth, Tony Jones, is summoned into the Moonlands as he is believed to be this Final Dreamer. He joins forces with the apprentice Magi, Edyn, and the Shadow Stalker, Strag, on a mission to gather the Dreamstones before Agram is set free. Using the Book of Elders, the three travel through the Moonlands while combatting the forces of Agram and gaining an ever-growing collection of Dream Creatures from the Moonlands that they visit.

The first episode shows a boy being given a jeweled ring by his grandfather, and later being transported to another world while participating in a footrace. He then meets another boy and a girl in the other world, who use magic stones with powers.

This cartoon has previously been asked about and IDed here.

Pretty sure this is Magi-Nation (2007-2010).

Three thousand years ago in the Moonlands, the Shadow Magi Agram was sealed inside the planet's Core by the Core Glyph and the Dreamstones which provided its power. Now he plans to escape by using his Shadow Geysers to weaken his prison in order to bring the Moonlands under his control, and only a Magi known as the "Final Dreamer" can stop him. A young boy from Earth, Tony Jones, is summoned into the Moonlands as he is believed to be this Final Dreamer. He joins forces with the apprentice Magi, Edyn, and the Shadow Stalker, Strag, on a mission to gather the Dreamstones before Agram is set free. Using the Book of Elders, the three travel through the Moonlands while combatting the forces of Agram and gaining an ever-growing collection of Dream Creatures from the Moonlands that they visit.

The first episode shows a boy being given a jeweled ring by his grandfather, and later being transported to another world while participating in a footrace. He then meets another boy and a girl in the other world, who have a magic book and wield magic stones that can summon monsters.

This series has previously been asked about and IDed here.