Main concepts and de nitions can be found in [1]. A quasigroup (Q;
) is said to be left-transitive if the identity xy
xz = yz holds [2]. The following results are obtained. Lemma 1. Any left-transitive quasigroup (Q;
) has a left unit, i.e., there exists an element f 2 Q such that f
x = x for all x 2 Q. Lemma 2. Any left-transitive quasigroup (Q;
) is an LIP-quasigroup. Theorem 1. Any loop, which is an isotope of left-transitive quasigroup (Q;
), is a group. Lemma 3. Any left-transitive quasigroup (Q;
) is isotopic to an abelian group if and only if translation Rf is an automorphism of the quasigroup (Q;
). Lemma 4. Any left-transitive quasigroup (Q;
) is a left F-quasigroup if and only if translation Rf is an automorphism of the quasigroup (Q;
). Lemma 5. Any left-transitive quasigroup (Q;
) is a left Bol quasigroup. Lemma 6. Any quasi-automorphism  of left-transitive quasigroup (Q;
) has the form = RkRf 0; where k is a xed element of the set Q, f is a left unit of the quasigroup (Q;
), 0 is an automorphism of (Q;
). Theorem 2. Any autotopy ( ; ; ) of left-transitive quasigroup (Q;
) has the form ( ; ; ) = (RfLk;Rd;LkRd)Rf ; where f is a left unit of the quasigroup (Q;
), k; d are the xed elements of the set Q,  is an automorphism of (Q;
).