What are the numbers in classical music titles?
When looking at a Classical piece, you may be confronted with a title like this:
Muzio Clementi - Sonata in G minor op 34 no 2 - III. Molto allegro
Each of those numbers has a meaning that helps us distinguish exactly which piece it is. This is necessary since most classical works are named after what genre they are (i.e. Sonata, Prelude, Minuet, Nocturne) rather than being given descriptive/unique titles.
(Sometimes, as in the above, the key (G minor) is included, but this is not necessary as far as the numbers are concerned, and more of a shortcut for musicians who remember the key but not the numbers.)
Opus
Opus, usually abbreviated to "op", literally means "work", as in "This is my 34th published work." It can refer to a single piece, but often refers to a collection of similar pieces published together. In that case, you will need:
Number
Number, usually abbreviated to "no" is the number of a piece within an opus. As in, "This is the 2nd sonata in my Opus 34 batch of sonatas." If the opus is only a single piece, no number is needed.
Numerals
Many classical works feature multiple movements, or individual pieces intended to be played together, each having music that somehow relates to the others. Movements are numbered with Roman numerals and named after their tempo/style directives.
For instance, the 3rd (III) movement of Clementi's Sonata opus 34 number 2 is marked "Molto allegro" (which translates to Very Lively, meaning it should be played with a particularly high speed and crispness). The 2nd movement, which comes before it, is marked Un poco adagio (which translates to A Little Slow, meaning a much more relaxed tempo than the 3rd movement, but not too sluggish), so it would be named II. Un poco adagio.
So, Sonata op 34 no 2 - III. Molto allegro refers to:
The 3rd (III) movement of the 2nd (no 2) sonata in the 34th publication (op 34) by Muzio Clementi.
Complications
Genre numbering. Some composers who have achieved particular prominence in a particular genre, such as Beethoven with his sonatas or Mozart with his symphonies, have those compositions numbered in chronological order of publication, alongside the actual opus and number. A good way to see this in action is looking through the Beethoven's Sonatas page on Wikipedia. For instance, the Moonlight Sonata could be called Sonata no. 14, because it's his 14th sonata. It could also be called op 27 no 2, because it's the 2nd sonata in his 27th opus.
Non-standard numbers and letters. Some composers/publishers did not keep track of their opus numbers, and their works are numbered by the person who eventually put them in order.
Mozart - Works were compiled by Ludwig von Köchel, so his last initial, K, is used alongside a number. Examples would include String Quintet in C major K.515 or Piano Sonata in G major K.283.
J. S. Bach - Works are compiled in the Bach Works Catalogue - in German, the Bach-Werke-Verzeichnis, giving us the initials BWV. For instance, the Prelude and Fugue in B flat minor from the first Well-Tempered Clavier book is marked BWV 867.
There are further complications and other systems, but this should provide a good context to understand most of what you encounter!