How Tempo, Dynamics and Expression can be Notated

Notation of Tempo

Tempo marks determine the speed of music. They are typically written at the beginning of a piece, and can be notated in two primary ways.
Metronome tempo markings indicating the exact beats per minute (BPM), for example: ♩=120, meaning the quarter note (crotchet) beats 120 times per minute.
Italian words are often used to define the speed of the piece like Allegro (Fast), Andante (Walking Speed), or Lento (Slow). These denote various speeds, but are more subjective.

Notation of Dynamics

Dynamics refer to how loud or soft the music should be played. These are also typically notated using Italian words.
To signify loudness, F (Forte) is used for loud and P (Piano) for soft.
These can be modified with other letters, such as mf (mezzo forte) to indicate moderately loud, or pp (pianissimo) for very soft.
Dynamics can change gradually with the use of a Crescendo (gradually get louder) or Diminuendo (gradually get softer). These are notated with specific signs.

Notation of Expression

Articulation marks are used to express how individual notes should be played. For example, a dot above a note head means the note is to be played staccato (short and detached), while a curved line connecting notes suggests legato (smooth and connected).
Expressive text in music can provide more detail about how the music should be performed. For example, con moto (with movement), or dolce (sweetly).
Symbols such as a Fermata (pause) over a note or rest instructs the performer to sustain the note longer than its given duration.
Slurs, ties, and accents can all contribute to the expressive qualities of a piece, each of these symbols have different effects on how notes are linked, sustained, or emphasised respectively.

Remember, all these notations are essentially the composer’s way of communicating how they envisage the piece to be interpreted and performed. Notations provide the framework, but the performer brings the piece to life.