EN
We describe, using elementary methods, the K\"othe dual of variable Lebesgue spaces \(L^{p(\cdot)},\) called also Nakano spaces, independenly for \(p(\cdot) \in (1, \infty)\) and \(p(\cdot) \in (0, 1)\). The case when \(p(\cdot) \in [1, \infty]\) is also included.