Lyapunov is a Russian surname that is sometimes romanized as Ljapunov, Liapunov or Ljapunow and may refer to:
- Prokopy Lyapunov (? –1611), Russian statesman
- Zakhary Lyapunov (? – after 1612), Russian statesman, Prokopy Lyapunov's brother
- Mikhail Lyapunov (1820–1868), Russian astronomer
- Aleksandr Lyapunov (1857–1918), Russian mathematician and mechanician
- Lyapunov equation
- Lyapunov exponent
- Lyapunov function
- Lyapunov fractal
- Lyapunov stability
- Lyapunov's central limit theorem
- Lyapunov vector
- Lyapunov (crater)
- Sergei Lyapunov (1859–1924), Russian composer
- Boris Lyapunov (1862–1943), Russian expert in Slavic studies
- Alexey Lyapunov (1911–1973), Russian mathematician