Aggettivi e pronomi dimostrativi

Demonstrative adjectives and pronouns indicate the person or the object being talked about. The Italian forms questo and quello correspond exactly to the English ‘this’ and ‘that’.
Questo indicates somebody or something that is near to the speaker in terms of space, time or mention in the discourse.
Quello indicates somebody or something that is far away from the speaker in terms of space, time or mention in the discourse.

Demonstratives agree in gender and number with the noun they refer to, and, when used as adjectives, they always precede it.

Like all the nouns and adjectives ending in –o, questo has four endings, reflecting agreement with the noun it refers to:
Questo libro - This book
Questi libri - These books
Questa casa - This house
Queste case - These houses

As an adjective, i.e. when attached to a noun, quello is used with masculine words beginning with /z/gn/pn/ps/x, or with s + consonant. The plural of quello is quegli.
Quello becomes quel with masculine words beginning with most consonants; the plural of quel is quei. The feminine form is quella/quelle.
Quello specchio/Quegli specchi - That mirror/Those mirrors
Quello zaino/ Quegli zaini - That rucksack/Those rucksacks
Quel libro/Quei libri - That book/Those books
Quel quadro/Quei quadri - That picture/Those pictures
Quella borsa/Quelle borse - That bag/Those bags

As a pronoun, i.e. when standing alone (pronoun=in place of the noun), quello shows four endings, according to the noun it implicitly refers to:
Quale vestito prendi? Prendo quello (= quel vestito)
Quali libri prendi? Prendo quelli (= quei libri)
Quale borsa prendi? Prendo quella (= quella borsa)
Quali penne prendi? Prendo quelle (= quelle penne)

Please note also that there is elision of questo, questa, and quello, quella before a word beginning with a vowel, independently of its gender.
Quest’aereo - This airplane
Quest’aula - This classroom
Quell’orologio - That watch
Quell’autostrada - That highway

Moreover, questa is sometimes shortened and contracted with the noun it modifies: questa sera > stasera this evening