All pieces

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Beginner

Amazing Grace (arranged for beginners) Traditional (American hymn tune "New Britain")
A well-known pentatonic melody with a one-beat pickup, in half, quarter and a few eighth notes, over a single sustained bass note per bar - gentle two-hand reading at a slow tempo.
Lullaby (arranged for beginners) Johannes Brahms (Wiegenlied, Op. 49 No. 4)
Brahms's Lullaby in 3/4: the tune in the right hand, from two eighth notes at the end of the first bar, over a left hand that holds C, F and G chords and breaks some of them into a rising arpeggio, one note a beat.
Waltz, Op. 39 No. 15 (theme, arranged for beginners) Johannes Brahms (Waltz in A-flat major, Op. 39 No. 15)
Brahms's best-known waltz in 3/4: a gentle tune over left-hand chords of G, C and D, most of them held, four of them broken into a rising arpeggio.
Greensleeves (arranged for beginners) Traditional (English, 16th century)
A well-known minor-key melody in quarters and eighths over a single sustained bass note per bar - reading two staves together at a gentle tempo.
In the Hall of the Mountain King (theme, arranged for beginners) Edvard Grieg (Peer Gynt Suite No. 1, Op. 46 No. 4)
Grieg's creeping theme in A minor: steady eighth notes over held chords of A minor and E major.
Jingle Bells (opening refrain, arranged for beginners) James Lord Pierpont
A very well-known, mostly repeated-note and stepwise melody in quarter/half notes over a single sustained bass note per bar, at a brisk tempo.
Mary Had a Little Lamb (arranged for beginners) Traditional (American, 19th century)
A very well-known three/four-note melody that never leaves a five-finger hand position, over a single sustained bass note per bar - an easy first piece for a fixed hand position.
Minuet in G major (first part, arranged for beginners) Christian Petzold (attributed; Notebook for Anna Magdalena Bach, BWV Anh. 114)
The first part of the Minuet in G from the Notebook for Anna Magdalena Bach, played twice: the tune in quarters and even eighths over held chords of G, C and D.
Ode to Joy (theme, arranged for beginners) Ludwig van Beethoven
A simple stepwise melody with steady quarter notes over static left-hand chords - an easy introduction to playing both hands together.
Old French Song (arranged for beginners) Pyotr Ilyich Tchaikovsky (Album for the Young, Op. 39 No. 16)
Tchaikovsky's sad Old French Song in 2/4, from a one-eighth pickup: the tune over held chords of A minor, D minor and E major.
Twinkle, Twinkle, Little Star (arranged for beginners) Traditional (French, 18th century)
A very well-known stepwise-and-small-leap melody in quarter and half notes, over a single sustained bass note per bar - an easy first tune for reading two staves together.

Intermediate

Minuet in B-flat major, BWV Anh. 118
A minuet in B-flat major in which the hands take turns with the eighth notes (the left hand in bars 1-5 and 17-19, the right hand in bars 6-7 and 11-14), with appoggiaturas in bars 2 and 4 and a trill with a two-note ending in bar 10; both halves repeated, the first with first and second endings.
Douce Plainte (25 Etudes faciles, Op. 100, No. 16) Johann Friedrich Franz Burgmüller
A gentle lament in G minor, Allegro moderato: a long-breathed right-hand melody over left-hand broken chords in quiet, even sixteenth notes; later the right hand takes the sixteenths and staccato thirds.
Inquiétude (25 Etudes faciles, Op. 100, No. 18) Johann Friedrich Franz Burgmüller
Restlessness in E minor, Allegro agitato, 2/4: slurred groups of three sixteenth notes after a sixteenth rest in the right hand, each released on the rest, over short staccato chords in the left hand on the beats.
La Pastorale (25 Etudes faciles, Op. 100, No. 3) Johann Friedrich Franz Burgmüller
A shepherd's song in 6/8 in G major, Andantino: a singing right-hand melody in dotted quarters and eighths, with grace notes (bars 3, 5, 7, 19, 21, 26-27), over soft repeated eighth-note chords in the left hand.
Innocence (25 Etudes faciles, Op. 100, No. 5 - opening strain, arranged) Johann Friedrich Franz Burgmüller
A graceful right-hand melody mixing 16th-note turns with dotted-quarter/eighth figures over a sustained left-hand triad in each bar, in 3/4 at a moderate tempo - light articulation and phrase shading more than raw technique.
Für Elise (theme, arranged for this app) Ludwig van Beethoven
Melodic phrasing over a broken-chord left-hand accompaniment, with a chromatic neighbour-note motif.
Fur Elise (opening motif, easy arrangement) Ludwig van Beethoven
The famous opening motif at a gentle tempo with nothing faster than eighth notes, over a single left-hand bass note per bar.
Minuet in F major, K. 2 Wolfgang Amadeus Mozart
One of Mozart's earliest pieces, a graceful 3/4 dance in F major: broken-chord leaps in the right hand over a simple bass line and a triplet in bar 7.
Musette in D major, BWV Anh. 126
A bagpipe dance in 2/4 over a drone: the left hand leaps in octaves (on D, then A and E) and doubles the right hand in bars 3–4 and 7–8; the right hand has sixteenth-note runs and eighth-note figures.
Minuet in G major, BWV Anh. 114 Christian Petzold
Two independent lines in 3/4: a right-hand melody of stepwise eighth-note runs and leaps against a left hand that moves in its own line of mostly dotted-half, half and quarter notes; mordents (bars 3, 5, 11, 13), a grace note in bar 8 and a short trill in bar 30, and a second half that turns to D major (C sharp) before coming home.
Minuet in G minor, BWV Anh. 115 Christian Petzold
The G major minuet’s companion in the minor: the same two-line minuet texture in 3/4, reading B flat and E flat from the key, F sharp as the leading note, and E natural and B natural as the music passes through B flat major and F major before returning home; mordents (bars 13, 22) and short trills (bars 8, 9, 15, 31).

Advanced

La Candeur (25 Etudes faciles, Op. 100, No. 1) Johann Friedrich Franz Burgmüller
Sincerity in C major, Allegro moderato: an even, flowing line of eighth notes in the right hand over held chords (bars 1-8), then in the left hand under held thirds in the right (bars 9-12); in bar 13 the right hand holds a two-note melody above its own eighths.
Ballade (25 Etudes faciles, Op. 100, No. 15) Johann Friedrich Franz Burgmüller
A dramatic ballad in C minor: the tune in the left hand under light staccato chords in the right, then a singing middle part in C major, and the opening's drama again.
l'Arabesque (25 Etudes faciles, Op. 100, No. 2) Johann Friedrich Franz Burgmüller
Quick 16th-note turn figures answered by a light eighth-note tag, alternating with a lyrical dotted-quarter melody, over a steady broken-chord left hand in A minor - finger agility and voicing a short melodic cell cleanly at a scherzando tempo.
Prelude in C minor, Op. 28 No. 20 Frédéric Chopin
Dense four- and five-note block chords in both hands (up to an octave; the right hand's three ninths rolled), a full ff-to-pp dynamic range with two written crescendi, and a two-layer right-hand texture (a sustained chord against a decorative turn figure) that asks for careful voicing and pedalling rather than finger speed.
Prelude in E minor, Op. 28 No. 4 ("Largo") Frédéric Chopin
Chromatic voice leading, sustained dissonance, a wide dynamic range, and rhythmic independence between a slow-moving right-hand line and pulsing left-hand chords.
Prelude in B minor, Op. 28 No. 6 Frédéric Chopin
A slow lament in B minor whose melody lies in the left hand, like a cello, under soft repeated chords in the right hand; let the bass line sing and keep the right hand's chords even and quiet.
Sonatina in C major, Op. 36 No. 1 (1st movement) Muzio Clementi
A brisk single-line melody in the right hand (scale runs, octave leaps, broken octaves) over a light left hand of mostly quarter, half and whole notes, with broken-chord eighths in bars 9, 11, 32 and 34: an exposition that moves to G major, a short development that turns to C minor (bars 16-23), and the return in C - reading fluency and a fast, even tempo more than technical difficulty.
Für Elise, WoO 59 Ludwig van Beethoven
The whole rondo as Beethoven wrote it: the A theme over broken-chord bass, the F-major episode with its grace notes and 32nd-note figures, the agitated C section over a repeated bass pedal, and the triplet arpeggio run up under an 8va and back down chromatically.
In the Hall of the Mountain King Edvard Grieg
Grieg's own piano version of the trolls' march in B minor: the theme creeps up from the bass in short, detached eighth notes, pianissimo, and comes back again and again, climbing and growing (it starts over, pianissimo, at bar 18); Più vivo (quarter = 154) from bar 50 and sempre stretto from bar 58 drive it to full chords in both hands.
Morning Mood Edvard Grieg
Grieg's own piano version of the sunrise from Peer Gynt: a pastoral 6/8 melody passed between the hands over held chords and wide left-hand chords, the tenths rolled, the forte climax in full chords, the left-hand melody under right-hand figuration, trills with their endings, and the quiet return over a pedal note.
Morning Mood (easier chords) Edvard Grieg
Grieg's own piano version of the sunrise from Peer Gynt with every chord inside one hand's reach: the pastoral 6/8 melody over held triads, the forte climax, the left-hand melody under right-hand figuration, trills with their endings, and the quiet return.
Gymnopedie No. 1 Erik Satie
A wide-spanning left hand alternating a low bass note with a chord high above it (up to a two-and-a-half-octave leap), unmarked, player-chosen pedalling, ties held across barlines and soft, patient dynamic shading (pp/p/f) at a slow tempo.
March of the Wooden Soldiers (Album for the Young, Op. 39, No. 5) Pyotr Ilyich Tchaikovsky
A toy soldiers' march in D major, Tempo di Marcia: crisp staccato chords and dotted rhythms in the right hand over a marching left hand, quick and precise at quarter = 140, with a drum figure of repeated A's in the left hand (bars 8, 16 and 40).