Mnogo mi se sviđa ova pesma.

Serbian often expresses to like with the verb sviđati se, which works more like to be pleasing to.

So this sentence is structured more like:

This song is very pleasing to me

than like:

I like this song

That is why the grammar looks different from English.

Serbian also has voleti, and Volim ovu pesmu is possible, but sviđa mi se is a very common way to say that something appeals to you or that you like it.

Mi means to me.

It is the short, unstressed dative form of ja.

• mi = to me
• full form: meni

In this sentence, mi shows who experiences the liking:

• Mnogo mi se sviđa ova pesma = I like this song very much
• literally: This song is very pleasing to me

If you want extra emphasis, you can use meni instead:

• Meni se sviđa ova pesma.

Se is part of the verb expression sviđati se.

In many Serbian verbs, se is not translated word-for-word into English. It is simply part of how the verb is used, so it is best to learn the verb as a whole:

• sviđati se = to be pleasing / to appeal / to be liked

So do not think of sviđa by itself as the full verb here. The pattern is:

• sviđati se nekome = to be pleasing to someone

Because ova pesma is the grammatical subject of the sentence, so it stays in the nominative case.

With sviđati se, the thing you like is treated as the thing that pleases you.

So:

• ova pesma = nominative, the thing doing the pleasing
• mi = dative, the person receiving that feeling

Compare:

• Sviđa mi se ova pesma.
  Literally: This song pleases me.

but:

• Volim ovu pesmu.
  Literally: I love/like this song.

In the second sentence, ovu pesmu is a direct object, so it is in the accusative.

Because the verb agrees with ova pesma, not with I.

The subject is ova pesma, which is third person singular, so the verb is also third person singular:

• ova pesma se sviđa → sviđa

It is not sviđam, because I am not the grammatical subject here.

A useful comparison:

• Sviđam ti se. = You like me.
  Literally: I am pleasing to you.

Here the subject is I, so the verb is sviđam.

Because mi and se are clitics. In Serbian, clitics usually go in second position in the clause.

In this sentence, the first element is Mnogo, so the clitics come right after it:

• Mnogo mi se sviđa ova pesma.

But Serbian word order is flexible, so you can also say:

• Ova pesma mi se mnogo sviđa.

That is also natural. Here the first element is Ova pesma, and the clitics come after that phrase.

What is usually not natural is placing the clitics randomly, for example after the main verb.

Here mnogo means very much or a lot.

It strengthens the sentence:

• Sviđa mi se ova pesma. = I like this song.
• Mnogo mi se sviđa ova pesma. = I like this song very much.

You can also hear other intensifiers, such as:

• jako mi se sviđa = I like it a lot / very much
• baš mi se sviđa = I really like it

But mnogo is very common and natural.

The dictionary form is usually sviđati se.

This is the imperfective verb, and it is the one used for a general, ongoing state like I like it.

There is also a perfective partner:

• sviđati se = imperfective
• svideti se = perfective

In this sentence, the present tense sviđa mi se expresses a current state or general feeling, so the imperfective is the right choice.

A rough idea of the difference:

• Sviđa mi se ova pesma. = I like this song.
• Pesma mi se svidela. = I liked the song / the song appealed to me.

The second one often refers to a completed impression, for example after hearing it.

It can be rearranged, because Serbian word order is fairly flexible.

All of these can be natural, depending on emphasis:

• Mnogo mi se sviđa ova pesma.
• Ova pesma mi se mnogo sviđa.
• Mnogo se mi sviđa ova pesma. is not natural, because the clitics are misplaced.

The main things to keep in mind are:

1. mi and se usually stay together as clitics
2. they usually come in second position
3. moving ova pesma or mnogo can change emphasis

For example:

• Ova pesma mi se mnogo sviđa. puts more focus on this song
• Mnogo mi se sviđa ova pesma. puts more focus on very much