  Motivated by recent results on the constructions of permutation polynomials
with few terms over the finite field $\mathbb{F}_{2^n}$, where $n$ is a
positive even integer, we focus on the construction of permutation trinomials
over $\mathbb{F}_{2^n}$ from Niho exponents. As a consequence, several new
classes of permutation trinomials over $\mathbb{F}_{2^n}$ are constructed from
Niho exponents based on some subtle manipulation of solving equations with low
degrees over finite fields.
