Summary: The Unbounded Knapsack Problem (UKP) is a well-known variant of the famous 0-1 Knapsack Problem (0-1 KP). In contrast to 0-1 KP, an arbitrary number of copies of every item can be taken in UKP. Since UKP is NP-hard, fully polynomial time approximation schemes (FPTAS) are of great interest. Such algorithms find a solution arbitrarily close to the optimum \(\mathrm{OPT}(I)\), i.e., of value at least \((1-\varepsilon)\mathrm{OPT}(I)\) for \(\varepsilon>0\), and have a running time polynomial in the input length and \(\frac{1}{\varepsilon}\). For over thirty years, the best FPTAS was due to Lawler with running time \(O(n+\frac{1}{\varepsilon^3})\) and space complexity \(O(n+\frac{1}{\varepsilon^2})\), where \(n\) is the number of knapsack items. We present an improved FPTAS with running time \(O(n+\frac{1}{\varepsilon^2}\log^3\frac{1}{\varepsilon})\) and space bound \(O(n+\frac{1}{\varepsilon}\log^2\frac{1}{\varepsilon})\). This directly improves the running time of the fastest known approximation schemes for Bin Packing and Strip Packing, which have to approximately solve UKP instances as subproblems.