There are two basic kinds of comparisons that we make. We can say that things are unequal or equal. In these sentences we are dealing with "inequality".

In dealing with inequalities, we compare either adjectives or nouns. By this I mean, we say that someone (or something) is "bigger", "prettier", "better", "more interesting", etc. than someone or something else. Notice that in English we add "-er" to an adjective in some cases, but in others, we say "more". In general, when the adjective is more than two syllables long we use "more" rather than adding "-er". There is no ending such as "-er" in Spanish. We simply use más (more).

There are just a few exceptions, such as mejor (better), mayor (older), peor (worse), and menor (younger).

Here are some of the exceptions for the comparison of adjectives.

good     bueno      old       viejo
better   major      older     mayor

bad      malo       young     joven
worse    peor       younger   menor

Then we indicate the person or thing that we are comparing to, by the word "that". In Spanish, this is normally "que" (the same word we use for "that").

For example:

Mary is smarter than her sister.
María es más inteligente que su hermana.

Notice that in this case we are comparing the "qualities" that adjectives describe, such as "goodness", "smartness", "prettiness", "badness", etc.

There is another kind of comparison that we can make. In this case, we aren't comparing "qualities", but rather "quantities". For example, we might say:

Mary has read more books than her sister.
María ha leído más libros que su hermana.

Notice that "her" sister doesn't directly state a number of books. We are not comparing "books" to "sister". What we really mean is that "Mary has read more books than her sister has read". The quantity of books we are using for the comparison is suggested, but not actually stated. If we actually state the quantity of books we are comparing to, we would use "de" for "that", not "que".

Mary has read more than ten books.
María ha leído más de diez libros.

Ten books is a direct statement of the quantity of books that we are using for the standard of comparison. Often there is a specific number used in this pattern which might be a good cue that we should use "de" instead of "que" for translating the word "that".

There is one case in which we directly state the "standard" for the comparison of quantity, but we don't put an actual number on it. Let's take a quick look at this pattern.

Mary has read more books than those that her sister has read.
María ha leído más libros de los que su hermana ha leído.

You probably noticed that "los" must match "los libros". We could have this same pattern using "del que", "de la que", or "de las que", depending on the noun that we are matching. In the case of the singular form, in English we would normally use "that which" or "the one which" instead of "the ones".

Mary has spent more money than that which her sister has spent.
María ha gastado más dinero del que su hermana ha gastado.