Many of my students are confused 이에요 and 있어요, so I am writing this post to make sure you understand 이에요 and 있어요.
이에요means “something/someone is/are/am a noun”. For example,
저는 한국 사람이에요. I am Korean.
(이 분이) 제 선생님이에요. This person is my teacher.
한국어 책이에요. It is a Korean book.
여기가 도서관이에요. Here is the library.
이게 제 가방이에요. This is my bag.

On the other hand, 있어요 has two different meanings. The first meaning is “have(possession)“, and the other one is “is/am/are at/in/on somewhere(existence)“. It is not just ‘is’, it means ‘is at/in/on somewhere(existence)‘.

Let’s look at some examples.
(저는) 한국 친구가 있어요. I have Korean friends. (possession)
시간이 많이 있어요. I have a lot of time. (possession)
앤디 씨는 가방이 많이 있어요. Andy has a lot of bags. (possession)
앤디 씨 집에 가방이 많이 있어요. At Andy’s house, there are lots of bags. (existence)
미나 씨가 집에 있어요. Mina is at home. (existence)
마이크 씨가 한국에 있어요. Mike is in Korea. (existence)
제 집이 도서관 앞에 있어요. My house is in front of the library. (existence)
책상에 책이 있어요. There is a book on the desk.(existence)
교실 옆에 화장실이 있어요. There is a bathroom next to the classroom. (existence)

As you can see, when 있어요 means “be at some place“, 있어요 follows after “-에” which is a place particle.

Let’s look at these two sentences.
1. 여기가 도서관이에요. Here is the library.
2. 제 집이 도서관 앞에 있어요. My house is in front of the library.

In these two sentences, 이에요 and 있어요 are used with a noun(place), however, 이에요 means “is a noun” while 있어요 means “is at a place”

Do you know what the opposite word of 이에요? It is 아니에요(is not a noun). You can learn 아니에요 by clicking here.

How about the opposite word for 있어요? It is 없어요. For more examples of -에 있어요/없어요 by clicking here. For more examples of 있어요(possession) by clicking here.

i.e)