That looks to be quite a shallow pot its growing in, unless we can only see the top of it, so repotting into something with a little more depth might be useful, using new potting soil.
When you water, do you empty out the outer pot after 30 minutes if there's any sitting in there? If not, then do so - water when the surface of the soil feels just about dry to the touch, water thoroughly, allowing the excess to drain away freely from the bottom of the pot. And empty out the outer pot 30 minutes later so its not left sitting in water.
It is a Hedera helix variety, not sure which. When you repot, or if you don't, turn it out of its pot and inspect the roots/rootball for signs of invaders, just to make sure there's nothing that shouldn't be there at the root.
Otherwise, has it been in direct sun? If so, remove it from direct sunlight - it will prefer medium to bright daylight and relatively cool temperatures. If the humidity is very low indoors, that can cause browning at the edge of the leaves, so don't stand it near any heat source (radiator, computer and so on). Otherwise, it looks relatively healthy, evidenced by the new and glossy leaves growing at the top.
UPDATE: Now you've posted an image showing the whole pot and the plant, far from the pot it's in being too shallow, it's actually too large. It's always best to pot up by one or two sizes at most; too large of a pot means a lot of soil that is unoccupied by roots, yet you need to keep that soil moist or the small rootball of the plant dries out. This means the plant is either sitting in sour, waterlogged soil, or has insufficient water - either way, it suffers. I suggest you repot into something of a more suitable size, then move it into the larger pot once its grown on some.