The articles.

Articles are written before a name, and have the same genere (genre) and numero (number, meaning plural or singular) of that name. They are divided into definited (determinativo) and undefinited (indeterminativo) and they specify this characteristic of the name too: they tell us if the name is determinated or undeterminated.

ARTICOLI DETERMINATIVI: used to refer to a specific name, or a name already mentioned. They are: il, lo, la, i, gli, le, (l’) (all translated with the)

- Dammi il libro. | Give me the book. 

-How to use them:

.IL = male, singular. I = male, plural. They are used in front of names starting with consonants like:

il tavolo (the table), il pallone (the balloon)
i tavoli (the tables), i palloni (the balloons)

.The names starting with z, x, s+consonant, ps, pn, g and i (rarely, when considered semiconsonant) are usually preceded by LO (singular, male) and GLI (plural, male), for example:

lo zaino (the backpack), lo studio (the study), lo psicologo (the psychologist), lo gnomo (the dwarf), lo iato (the hiatus)
gli zaini (the backpacks), gli studi (the studies), gli psicologi (the psychologists), gli gnomi (the dwarves), gli iati (the hiatuses)

.Before names starting with vowels, are equally used LO (singular and male - used this time in the form of L’, to avoid the presence of two close vowels) and GLI (plural and male).

l’albero (the tree), l’invitato (the guest)
gli alberi (the trees), gli invitati (the guests)

.LA = female, singular. LE = female, plural. These are used in front of names starting with consonants and vowels too. In this last case, LA becomes L’.

la mamma (the mum), la casa (the house), l’anima (the soul)
le mamme (the mums), le case (the houses), le anime (the souls)

ARTICOLI INDETERMINATIVI: used to refer to a generic name or something unknown at the moment of the speech (something not mentioned before). They are: un, uno, una, un’ (translated with an, one, a). There is no plural version, so, in case of plural names, we use the articolo partitivo:  dei, degli, delle, or the aggettivo indefinito (undefined adjective) like alcuni, alcune, qualche (all these plurals, articles and adjectives, can be translated as some, a few..).

- Dammi un libro. | Give me a book.

-How to use them:

UN works as IL. It’s male and singular, used in front of names starting with consonants:

un tavolo (a table), un pallone (a balloon)

UNO works as LO: used in front of names starting with z, x, s+consonant, ps, pn, g and i (rarely, when considered semiconsonant). Male and singular.

uno zaino (a backpack), uno gnomo (a dwarf)

UNA works as LA, in front of names starting with consonants and i (rarely when considered semiconsonant). In front of names starting with vowels (except i as semiconsonant) becomes UN’.

una casa (a house), una foto (a photo), un’amica (a friend), una mela (an apple)

Plurals with the articoli partitivi or aggettivo indefinito:
To help you remember the articoli partitivi, you can try this:
dei = de + i (articolo determinativo plural corresponding)
degli = de + gli (articolo determinativo plural corresponding)
delle = de + le (articolo determinativo plural corresponding, but with the double l)
but remember that almost this way, you get the preposizioni articolate* that are a different thing.

dei/alcuni tavoli (some tables), dei/alcuni palloni (some balloons), degli/alcuni zaini (some backpacks), degli/alcuni gnomi (some dwarves), delle/alcune case (some houses), delle/alcune foto (some photos), delle/alcune amiche (some friends), delle/alcune mele (some apples.

Using qualche, the name stays singular but conceptually becomes plural: qualche tavolo = some tables, qualche amica = some friends, qualche mela = some apples, qualche gnomo = some dwarves….

Ho portato qualche amica / delle (alcune) amiche. | I took some friends. (female)
Ho portato qualche amico / degli (alcuni) amici. | I took some friends. (male)

Honestly, very rarely, you can even leave the plural name alone without adding the plural article (not the articolo partitivo and not the aggettivo indefinito).

Avete (dei) dubbi? (or just Dubbi?) | Do you have any doubt? (Doubts?)

ARTICOLI PARTITIVI: singular = del, dello, della; plural = dei, degli, delle.
Used as singular, with singular names, it refers to an undefined amount of that name (considered as a total), a bit of something.

Vorrei del prosciutto. | I’d like a bit of/some ham.
Vorrei del vino. | I’d like a bit of/some wine.
Mangerò della carne. | I will eat a bit of/some meat. 

*PREPOSIZIONI ARTICOLATE: (articulated preposition). These are born from a combination of articolo determinativo + preposizione semplice (simple preposition) as in the tab:

The preposizioni articolate follow the same rules as the ones of the article they are born from: 

il tavolo (the table) = del tavolo (of the table), lo zaino (the backpack) = dello zaino (of the backpack), le foto (the photos) = delle foto (of the photos)…

BEWARE ——> these prepositions are a different thing from the articles.
preposizione articolata  ≠ articolo partitivo, they have a different use and meaning.

C’erano delle foto sul tavolo. | There were some photos on the table.
=> (articolo partitivo: delle foto = alcune foto, some photos)
I proprietari delle foto erano felici. | The owners of the photos were happy.
=> (preposizione articolata: delle foto = of the photos)

The complete list of the simple preposition (preposizioni semplici) is: di (of), a (to), da (from), in (in), con (with), su (on), per (for), tra, fra (between). The last 3 are used with articles as well, but they don’t form new words as the ones in the tab do:

Ti ho visto tra la folla. | I saw you between (in) the crowd.