Mater filiam maxime amat.

Because Latin usually shows grammatical function with endings, not mainly with word order.

• mater is nominative singular, the case normally used for the subject.
• filiam is accusative singular, the case normally used for the direct object.

So even if the words moved around, mater would still be the one doing the loving, and filiam would still be the one being loved.

Because mater is a third-declension noun. Its basic dictionary form is already mater.

Its forms look like this:

• nominative: mater
• genitive: matris
• accusative: matrem

A learner coming from English sometimes expects feminine nouns to look like first-declension nouns, but Latin does not work that way. A noun can be feminine without belonging to the first declension.

filiam comes from filia, meaning daughter.

Since it is the direct object of amat, it has to be in the accusative singular. For a first-declension noun like filia, that accusative singular ending is -am.

So:

• filia = daughter, as a basic form
• filiam = daughter, as the direct object

amat is the third-person singular present active indicative of amare, to love.

The ending -t tells you the subject is he/she/it. Since mater is singular, the verb is singular too:

• amo = I love
• amas = you love
• amat = he/she loves

So mater ... amat means mother loves.

maxime is an adverb. Here it modifies the verb amat.

In this sentence it means something like:

• very much
• most
• especially

So maxime amat means loves very much or loves most.

It is important that maxime modifies the verb, not the noun. It does not mean that the daughter is somehow greatest or very big.

Yes. Latin word order is much more flexible than English word order because the endings already show each word’s job.

For example, these would still mean roughly the same thing:

• Mater filiam maxime amat
• Mater maxime filiam amat
• Filiam mater maxime amat

The basic meaning stays the same, but the emphasis can shift depending on which word comes first or last. In ordinary prose, putting the verb at the end, as here, is very common.

Because Classical Latin has no definite or indefinite article.

So:

• mater can mean mother, a mother, or the mother
• filiam can mean daughter, a daughter, or the daughter

Context tells you which English article makes the most sense.

Latin often leaves that idea understood from context, especially with close family relationships.

So Mater filiam amat will usually be understood as A mother loves her daughter or The mother loves her daughter, unless the context suggests otherwise.

If Latin wanted to make her own explicit, it could say:

• Mater filiam suam amat

Here suam means her own and agrees with filiam.

So the version without suam is not wrong; it is simply less explicit.

It is an adverb.

You can tell because it modifies amat (loves), not filiam (daughter).

• maxime amat = loves very much
• if it were an adjective modifying filiam, it would need to agree with filiam in gender, number, and case, and it would look different

So in this sentence, maxime describes how the mother loves.