本文中，主要讲述通过紧束缚近似及其二次量子化，建立数学模型，来求解单层石墨烯（SLG）、双层石墨烯（BLG）、双层有夹角的石墨烯（TBG）的能带结构。在对SLG的模型构建中，我们考虑到了次近邻间的耦合强度，得出其能量色散关系解析式，其结果与已有的科研文献结果相符的很好。对于BLG，其能量色散关系为二次型，层间加置偏压后，其能带将会打开一个可调控的能隙。我们在计算TBG的模型后，得出其结果与AB堆垛方式的BLG不一样，倒和SLG有相同之处。我们得到：（a）费米面附近的能量呈线性色散关系；（b）层间外加偏压后，不会打开能隙；（c）层间耦合作用越强，低能区的两个范霍夫奇异点的距离越近；（d）小角度时，TBG的费米速度随层间夹角变大而变大，逐渐趋近SLG的费米速度。然而TBG的理论结果（d）与最新的实验结果不符合，因此我们对模型做出了相关修正。

In this thesis, we studied the dispersion of the electronic bands in the single-layer graphene (SLG), bilayer graphene (BLG) and the twisted bilayer graphene (TBG) by the tight-binding approximation. For the calculation of SLG, we derive an analytic expression for the tight-binding dispersion including up to the second-nearest neighbors, and the results are consistent with what have been published in literature. For BLG, we find its dispersion of the electronic bands is quadratic. When applying a gate bias, we demonstrate that the electronic gap of BLG can be controlled externally. We consider a graphene bilayer with a relative small angle rotation between the layers. Contrary to what happens in an AA stacked bilayer and in accord with observations in monolayer graphene, we find: (a) the low energy dispersion is linear, as in a single layer; (b) an external electric field, perpendicular to the layers, does not open an electronic gap; (c) the more powerful the interlayer coupling is, the closer the distance is between two VHS; (d) the Fermi velocity of it can be significantly smaller than the single-layer value. However, based on the discrepancy between the model predictions in (d) and recent experiment results, thus the model is further revised in the article.