Today's omnipresent electronic circuits, chips, and memories are almost entirely based on silicon. Their development closely follows Moore's law, and many years of further miniaturization and development is foreseen in this technology. However, the limitations of silicon nanotechnology are becoming increasingly clear: high power consumption and the lack of integrable non-volatile memory are two of the key weaknesses. Several recent developments propose and investigate the application of magnetism for future logic and memory devices. Magnets are inherently good memories, and the flipping of spins consumes energy close to the lowest values allowed by thermodynamics. Among the most intensively researched magnetoelectronic devices are the Magnetic Random Access Memory (MRAM), the racetrack memory, as well as the magnetic Quantum-Dot Cellular Automata (MQCA), recently called nanomagnet logic (NML).  The QCA computing paradigm offers a new alternative to build logic and memory devices. Among several realizations, the NML is of interest in this work, which uses nanomagnets as basic building blocks to encode logic bits and switches in the magnetization state of ferromagnetic materials. An NML device is an array of closely spaced, dipole-coupled, single-domain nanomagnets designed for digital computation. NML offers very low power dissipation with high integration density of functional devices, as well as operates over a wide range of temperature. Basic structures, such as wires, inverters, and majority gate already have been demonstrated.  In this work, we present a detailed fabrication recipe to fabricate nanomagnets with good shape and size control. A complete logic component library is vital for digital logic design. Our ultimate goal is to realize novel logic elements to extend the library of nanomagnet logic circuits. Several building blocks are demonstrated already, such as wires, majority-logic gate, etc. We built new basic magnetic structures such as shape engineered majority gates, AND gate, OR gate, for the first time, and used wires, inverters and gates to construct more complex circuits, such as a fanout, an XOR, and a full adder. We propose NML designs, such as the complex gate, for even more complex structures for future testing. This work goes beyond the original MQCA concept in several ways, such as the building blocks have different aspect ratios and asymmetry to exploit the advantages of the shape engineered nanomagnet behavior.