讲座内容：

Drinfeld modules and Anderson $t$-motives form aparallel world, in finite characteristic, to the theory of abelian varietiesover global number fields. This analogy is far from complete: for example, thelattice of an Anderson $t$-motive can be ``smaller'' than it should be (i.e.,$\exp$ in (1) is not always an epimorphism, unlike the case of abelianvarieties in (2)).On the other hand, there is a natural notion of tensor product and Hom forAnderson $t$-motives, while their analogues for abelian varieties are not yetknown. There also exists an analogy between the theory of Anderson $t$-motivesand the theory of linear differential operators.We shall give the definitions of Anderson $t$-motives and related objects.First, we define the lattice $L(M)$ of a $t$-motive $M$, and the exact sequence\[0 \to L(M) \to \mathrm{Lie}(M) \xrightarrow{\exp} E(M). \tag{1}\]This is an analogue of the lattice exact sequence of a $g$-dimensional abelianvariety $A$:\[0 \to L(A)=\mathbb{Z}^{2g} \to \mathrm{Lie}(A)=\mathbb{C}^g \to A \to 0. \tag{2}\]Further, we will define the Tate modules $T_{\mathfrak p}(M)$, where $\mathfrak p$ isa prime ideal of a global function field, the Galois action on$T_{\mathfrak p}(M)$, eigenvalues of Frobenius automorphisms, and other relatedobjects.Finally, we will discuss some research problems.