The Triangulum Galaxy is a spiral galaxy 2.73 million light-years (ly) from Earth in the constellation Triangulum. It is catalogued as Messier 33 or NGC 598. The Triangulum Galaxy is the third-largest member of the Local Group of galaxies, behind the Andromeda Galaxy and the Milky Way. It is one of the most distant permanent objects that can be viewed with the naked eye.

The galaxy is the smallest spiral galaxy in the Local Group (although the smaller Large and Small Magellanic Clouds may have been spirals before their encounters with the Milky Way), and is believed to be a satellite of the Andromeda Galaxy or on its rebound into the latter due to their interactions, velocities, and proximity to one another in the night sky. It also has an H II nucleus.

The galaxy gets its name from the constellation Triangulum, where it can be spotted.

It is sometimes informally referred to as the "Pinwheel Galaxy" by some astronomy references, in some computerized telescope software, and in some public outreach websites. However, the SIMBAD Astronomical Database, a professional database, collates formal designations for astronomical objects and indicates that Pinwheel Galaxy refers to Messier 101, which several amateur astronomy resources including public outreach websites identify by that name, and that is within the bounds of Ursa Major.

Under exceptionally good viewing conditions with no light pollution, the Triangulum Galaxy can be seen with the 20/20 vision naked eye; to those viewers, it will sometimes be the farthest permanent entity visible without magnification. Its light diffuses (spreads) across a little more than a pinprick of the unmagnified sky, the cause of which is its broadness – this astronomers term a diffuse, rather than compact, object.

Observers range from finding the galaxy easily visible by direct vision in a truly dark (and impliedly dry, cloud-free) sky to needing to use averted vision in rural or suburban skies with good viewing conditions. It has been chosen as one of the critical sky marks of the Bortle Dark-Sky Scale, supported by its relative invariability, reasonable northern declination and brightness described.

The Triangulum Galaxy was probably discovered by the Italian astronomer Giovanni Battista Hodierna before 1654. In his work De systemate orbis cometici; deque admirandis coeli caracteribus ("About the systematics of the cometary orbit, and about the admirable objects of the sky"), he listed it as a cloud-like nebulosity or obscuration and gave the cryptic description, "near the Triangle hinc inde". This is in reference to the constellation of Triangulum as a pair of triangles. The magnitude of the object matches M33, so it is most likely a reference to the Triangulum Galaxy.

The galaxy was independently discovered by Charles Messier on the night of August 25–26, 1764. It was published in his Catalog of Nebulae and Star Clusters (1771) as object number 33; hence the name M33. When William Herschel compiled his extensive catalogue of nebulae, he was careful not to include most of the objects identified by Messier. However, M33 was an exception and he catalogued this object on September 11, 1784, as H V-17.

Herschel also catalogued the Triangulum Galaxy's brightest and largest H II region (diffuse emission nebula containing ionized hydrogen) as H III.150 separately from the galaxy itself; the nebula eventually obtained NGC number 604. As seen from Earth, NGC 604 is located northeast of the galaxy's central core. It is one of the largest H II regions known, with a diameter of nearly 1500 light-years and a spectrum similar to that of the Orion Nebula. Herschel also noted three other smaller H II regions (NGC 588, 592, and 595).

It was among the first "spiral nebulae" identified as such by Lord Rosse in 1850. In 1922–23, John Charles Duncan and Max Wolf discovered variable stars in the nebulae. Edwin Hubble showed in 1926 that 35 of these stars were classical Cepheids, thereby allowing him to estimate their distances. The results were consistent with the concept of spiral nebulae being independent galactic systems of gas and dust, rather than just nebulae in the Milky Way.

With a diameter of about 60,000 light-years, the Triangulum Galaxy is the third largest member of the Local Group of galaxies, roughly 60% the size of the Milky Way. It may be a gravitationally bound companion of the Andromeda Galaxy. Triangulum may be home to 40 billion stars, compared to 400 billion for the Milky Way, and 1 trillion stars for Andromeda Galaxy.

The disk of Triangulum has an estimated mass of (3–6) × 109 solar masses, while the gas component is about 3.2 × 109 solar masses. Thus the combined mass of all baryonic matter in the galaxy may be 1010 solar masses. The contribution of the dark matter component out to a radius of 55×103 ly (17 kpc) is equivalent to about 5 × 1010 solar masses.