  Let $\mathbb{F}_{q}$ denote the finite field of order $q,$ let
$m_1,m_2,\cdots,m_{\ell}$ be positive integers satisfying $\gcd(m_i,q)=1$ for
$1 \leq i \leq \ell,$ and let $n=m_1+m_2+\cdots+m_{\ell}.$ Let
$\Lambda=(\lambda_1,\lambda_2,\cdots,\lambda_{\ell})$ be fixed, where
$\lambda_1,\lambda_2,\cdots,\lambda_{\ell}$ are non-zero elements of
$\mathbb{F}_{q}.$ In this paper, we study the algebraic structure of
$\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ and their
dual codes with respect to the standard inner product on $\mathbb{F}_{q}^n.$ We
provide necessary and sufficient conditions for the existence of a self-dual
$\Lambda$-multi-twisted code of length $n$ over $\mathbb{F}_{q},$ and obtain
enumeration formulae for all self-dual and self-orthogonal
$\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}.$ We also
derive some sufficient conditions under which a $\Lambda$-multi-twisted code is
LCD. We determine the parity-check polynomial of all $\Lambda$-multi-twisted
codes of length $n$ over $\mathbb{F}_{q}$ and obtain a BCH type bound on their
minimum Hamming distances. We also determine generating sets of dual codes of
some $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ from the
generating sets of the codes. Besides this, we provide a trace description for
all $\Lambda$-multi-twisted codes of length $n$ over $\mathbb{F}_{q}$ by
viewing these codes as direct sums of certain concatenated codes, which leads
to a method to construct these codes. We also obtain a lower bound on their
minimum Hamming distances using their multilevel concatenated structure.
