Arnold推广了Poincare最后几何定理，提出了对辛微分同胚的Arnold猜想。Floer为了研究Arnold猜想，将Morse同调的理论向特定的道路空间做了推广，发展了Floer同调理论。基于Floer的想法，后来的一系列辛几何学家和几何拓扑学家发展了辛几何和几何拓扑的很多新技术。    
   
   本文介绍在不引入虚拟技术之前的Floer同调的构造和同调Arnold猜想的证明。在第一章，本文先回顾相关的辛几何概念。第二章介绍Arnold猜想，特别是同调Arnold猜想的研究进程和最近结果。
   
   为了对比，在第三章中，本文阐述了Morse同调的构造。在第四章，沿着和Morse同调相似的路径，本文逐步讨论了在Floer同调的过程中所用到的辛作用泛函的构造、轨线方程(Floer方程)的导出、指标的构造、模空间的性质、Floer同调群的导出。其中重点在于轨线模空间的流形结构的得出和紧性的分析。最后，利用Floer同调，本文给出了在虚拟技术出现前同调Arnold猜想的证明。

Arnold made a generalization for $Poincar\acute{e}$'s last geometric theorem and made a conjecture for Symplectomorphism.In order to study Arnold conjecture,Floer generalized Morse homology theory to specific loop spaces and developed the Floer theory.Besed on Floer's idea,many mathmaticians on symplectic geometry and goemetric topology developed many new techniques in symplectic geometry and goemetric topology.
  
  This paper gives an introduction to construction of Floer homology before appearance of Virtual techniques and a proof of homological Arnold conjecture.In the first part,this paper retrospects relative concepts of symplectic geometry.In the second part,the paper introduces the studying processes and recent results of Arnold conjecture,especially homological Arnold conjecture.
    
    For contract,the third part is an introduction for construction of Morse homology theory.In the forth part,along the similar way of morse homology,the paper discusses the processes of floer homology including construction of symplectic action functional,the derivation of function of trajectories(Floer function),the constrction of index,the properties of moduli spaces,the derivation of Floer homology group.The key point is the manifold structure of trajectories moduli spaces and analysis of compactness.Finally,the paper gives a proof of homological Arnold conjecture before appearance of Virtual techniques.